In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals re...In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals renormalization group(NORG)method,we revisit the problem of a quantum magnetic impurity coupled with a conventional s-wave superconductor.Here we present a detailed study focusing on the impurity spin polarization and susceptibility,the Kondo screening cloud,as well as the number and structures of the active natural orbitals(ANOs).In the superconducting phase,the impurity spin is partially polarized,indicating that the impurity remains partially screened by the quantum fluctuations.Furthermore,the impurity spin susceptibility becomes divergent,resulting from the presence of residual local moment formed at the impurity site.Correspondingly,a non-integral(incomplete)Kondo cloud is formed,although the ground state is a spin doublet in this phase.In comparison,the Kondo cloud is complete in the Kondo singlet phase as expected.We also quantify the critical point,where the quantum phase transition from a Kondo singlet phase to a superconducting phase occurs,which is consistent with that in previous works.On the other hand,it is illustrated that only one ANO emerges in both quantum phases.The structures of the ANO,projected into both the real space and momentum space,are distinct in the Kondo singlet phase from that in the superconducting phase.More specifically,in the Kondo singlet phase,the ANO keeps fully active with half-occupied,and the superconducting gap has negligible influence on its structure.On the contrary,in the superconducting phase,the ANO tends to be inactive and its structure changes significantly as the superconducting gap increases.Additionally,our investigation demonstrates that the NORG method is reliable and convenient to solve the quantum impurity problems in superconductors as well,which will promote further theoretical studies on the Kondo problems in such systems using numerical methods.展开更多
Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic ...Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic orbits or limit cycles.Interesting normal forms could be derived through a generalization of the concept'resonance',which offers nontrivial analytic approximations.Compared with traditional techniques such as multi-scale methods,the current scheme proceeds in a very straightforward and simple way,delivering not only the period and the amplitude but also the transient path to limit cycles.The method is demonstrated with several examples including the Duffing oscillator,van der Pol equation and Lorenz equation.The obtained solutions match well with numerical results and with those derived by traditional analytic methods.展开更多
A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most s...A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence,which does not require any sophisticated analysis like Cole-Hopf transformation or Painlevétest.New exact solutions of typical NPDEs are computed with this novel method,including one-and two-soliton(solitary wave)solutions,periodic solutions of exponential or elliptic function type.Moreover,exact reduced equations may also be conveniently computed for further analysis.展开更多
During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstru...During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.展开更多
Over the last decade,nuclear theory has made dramatic progress in few-body and ab initio many-body calculations.These great advances stem from chiral efective feld theory(xEFT),which provides an efcient expansion and ...Over the last decade,nuclear theory has made dramatic progress in few-body and ab initio many-body calculations.These great advances stem from chiral efective feld theory(xEFT),which provides an efcient expansion and consistent treatment of nuclear forces as inputs of modern many-body calculations,among which the in-medium similarity renormalization group(IMSRG)and its variants play a vital role.On the other hand,signifcant eforts have been made to provide a unifed description of the structure,decay,and reactions of the nuclei as open quantum systems.While a fully comprehensive and microscopic model has yet to be realized,substantial progress over recent decades has enhanced our understanding of open quantum systems around the dripline,which are often characterized by exotic structures and decay modes.To study these interesting phenomena,Gamow coupled-channel(GCC)method,in which the open quantum nature of few-body valence nucleons coupled to a deformed core,has been developed.This review focuses on the developments of the advanced IMSRG and GCC and their applications to nuclear structure and reactions.展开更多
We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode rep...We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.展开更多
Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and therma...Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and thermal diffusivity are derived.展开更多
With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Ya...With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.展开更多
In the present paper, we study effect of the long-range Coulomb interaction on the thermodynamic propertiesof graphene by renormalization group methods.Our calculations show that both the specific heat and the magneti...In the present paper, we study effect of the long-range Coulomb interaction on the thermodynamic propertiesof graphene by renormalization group methods.Our calculations show that both the specific heat and the magneticsusceptibility of the material behave differently from the Landau Fermi liquid.More precisely, we find that thesequantities are logarithmically suppressed with respect to its noninteracting counterpart when temperature is low.展开更多
We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improv...We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.展开更多
This paper presents the application of the renormalization group （RG） methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equation...This paper presents the application of the renormalization group （RG） methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equations, and then obtain the approximate solutions by solving the corresponding RG equations. It shows that the approximate solutions obtained from the RG method are superior to those from the conventionally perturbation methods.展开更多
We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on ...We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.展开更多
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced.A system of integro-differential equations for the cutoff-dependent potential is obta...The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced.A system of integro-differential equations for the cutoff-dependent potential is obtained.As an illustration,a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained.The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.展开更多
We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically th...We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R<sub>1</sub> and R<sub>2 </sub>of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.展开更多
We focus on the interpretability of deep neural networks(DNNs).DNNs are currently the most widely used models in the field of artificial intelligence.However,they have been considered to lack interpretability.The most...We focus on the interpretability of deep neural networks(DNNs).DNNs are currently the most widely used models in the field of artificial intelligence.However,they have been considered to lack interpretability.The most significant advantage of DNNs is that they can extract the features from big data effectively.The renormalization group(RG)is a kind of method in statistical physics.Physics research has shown that this method can effectively derive the macroscopic features from the microscopic characteristics of statistical physical systems.The coarse-graining procedure of the real-space RG is quite similar to the calculation in the forward propagation of DNNs.Inspired by this viewpoint,we consider establishing a corresponding relationship between the training process of the DNNs and RG.We propose a new framework to study the interpretability of DNNs using the RG method,and our main results are as follows:(1)Considering the input data and the main features extracted by a DNN as two statistical physical systems,we propose a rigorous correspondence relationship between the RG of input data and the training process of the DNN.Therefore,the DNN can be seen as a system artificially defined by its parameters,which carries out a non-canonical RG process on the data.(2)We prove that,when the input dataset is the one-dimensional Ising model,after the training process of the fully connected DNN,the limit of the coupling constant in the partition function of the network output is the same as the stable fixed point of the coupling constant calculated by the real-space RG on the input dataset.This shows that the ability of feature extraction of the DNN originates from the equivalence between their training process and the canonical RG.Also,both the DNN and RG extract the same macroscopic features from the data,which are the contents actually learned by the DNN.展开更多
In this study,we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials.This ab ini...In this study,we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials.This ab initio many-body computational toolkit,termed Zen,utilizes the VASP and Quantum ESPRESSO codes to perform first-principles calculations and generate band structures for realistic materials.The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers:the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperatures.To validate the performance of this toolkit,we examine three representative cases:correlated metal SrVO_(3),unconventional superconductor La_(3)Ni_(2)O_(7),and Mott insulator MnO.The calculated results exhibit excellent agreement with previously available experimental and theoretical findings.Thus,it is suggested that the Zen toolkit is proficient in accurately describing the electronic structures of d-electron correlated materials.展开更多
Understanding the formation of novel pair density waves(PDWs)in strongly correlated electronic systems remains extremely challenging.Recent mean-field studies suggest that PDW phases may arise in strong-coupling multi...Understanding the formation of novel pair density waves(PDWs)in strongly correlated electronic systems remains extremely challenging.Recent mean-field studies suggest that PDW phases may arise in strong-coupling multiband superconductors by the quantum geometric properties of paired electrons.However,scrutiny through sophisticated many-body calculations has been lacking.Employing large-scale density matrix renormalization group calculations,we obtain in the strong-coupling regime phase diagram as a function of doping concentration and a tuning interaction parameter for a simple two-orbital model that incorporates quantum geometric effects.The phase diagram reveals a robust PDW phase spanning a broad range of parameters,characterized by a Luttinger parameter K_(sc)~0.3 and the absence of coexisting competing spin or charge density wave orders.The observed pairing field configuration aligns with the phenomenological understanding that quantum geometry can promote PDW formation.Our study provides the most compelling numerical evidence to date for quantum-geometry-facilitated intrinsic PDW order in strongly correlated systems,paving the way for further exploration of novel PDW orders and quantum geometric effects in such systems.展开更多
In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any...In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any order.2)We will refer that the RG procedure can,in fact,be used to get the normal form of differential dynamical systems.3)We will also present the approximating center manifolds of the perturbed systems,and investigate the long time asymptotic behavior by means of RG formula.展开更多
We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-c...We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.展开更多
A magnetic impurity embedded in a Fermi sea is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale TK,the Kondo temperature,through the mechanism of the...A magnetic impurity embedded in a Fermi sea is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale TK,the Kondo temperature,through the mechanism of the Kondo effect.We have reinvestigated the Kondo singlet by means of the newly developed natural orbitals renormalization group(NORG)method.We find that,in the framework of natural orbitals formalism,the Kondo screening mechanism becomes transparent and simple,while the intrinsic structure of a Kondo singlet is clearly resolved.For a single impurity Kondo system in whichever case of either finite size or thermodynamic limit,there exists a single active natural orbital that screens the magnetic impurity dominantly.In the perspective of entanglement,the magnetic impurity is entangled dominantly with the active natural orbital,i.e.,the subsystem formed by the active natural orbital and the magnetic impurity basically disentangles from the remaining system.We have also studied the structures of the active natural orbital respectively projected into real space and momentum space.Moreover,the dynamical properties,represented by one-particle Green’s functions defined at the active natural orbital,are obtained by the correction vector method.Meanwhile,the well-known Kondo resonance is clearly observed in the spectral function at the active natural orbital.To realize the thermodynamic limit,the Wilson chains with the numerical renormalization group approach are employed.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12104247 and 11934020)。
文摘In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals renormalization group(NORG)method,we revisit the problem of a quantum magnetic impurity coupled with a conventional s-wave superconductor.Here we present a detailed study focusing on the impurity spin polarization and susceptibility,the Kondo screening cloud,as well as the number and structures of the active natural orbitals(ANOs).In the superconducting phase,the impurity spin is partially polarized,indicating that the impurity remains partially screened by the quantum fluctuations.Furthermore,the impurity spin susceptibility becomes divergent,resulting from the presence of residual local moment formed at the impurity site.Correspondingly,a non-integral(incomplete)Kondo cloud is formed,although the ground state is a spin doublet in this phase.In comparison,the Kondo cloud is complete in the Kondo singlet phase as expected.We also quantify the critical point,where the quantum phase transition from a Kondo singlet phase to a superconducting phase occurs,which is consistent with that in previous works.On the other hand,it is illustrated that only one ANO emerges in both quantum phases.The structures of the ANO,projected into both the real space and momentum space,are distinct in the Kondo singlet phase from that in the superconducting phase.More specifically,in the Kondo singlet phase,the ANO keeps fully active with half-occupied,and the superconducting gap has negligible influence on its structure.On the contrary,in the superconducting phase,the ANO tends to be inactive and its structure changes significantly as the superconducting gap increases.Additionally,our investigation demonstrates that the NORG method is reliable and convenient to solve the quantum impurity problems in superconductors as well,which will promote further theoretical studies on the Kondo problems in such systems using numerical methods.
文摘Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic orbits or limit cycles.Interesting normal forms could be derived through a generalization of the concept'resonance',which offers nontrivial analytic approximations.Compared with traditional techniques such as multi-scale methods,the current scheme proceeds in a very straightforward and simple way,delivering not only the period and the amplitude but also the transient path to limit cycles.The method is demonstrated with several examples including the Duffing oscillator,van der Pol equation and Lorenz equation.The obtained solutions match well with numerical results and with those derived by traditional analytic methods.
基金supported by the National Natural Science Foundation of China under Grant No.12375030the National Natural Science Foundation of China under Grant No.12471084.
文摘A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence,which does not require any sophisticated analysis like Cole-Hopf transformation or Painlevétest.New exact solutions of typical NPDEs are computed with this novel method,including one-and two-soliton(solitary wave)solutions,periodic solutions of exponential or elliptic function type.Moreover,exact reduced equations may also be conveniently computed for further analysis.
基金the National Natural Science Foundation of China(Grant No.51534002)the Special Funds for Technological Innovation and Entrepreneurship of China Coal Science and Engineering Group Co.Ltd.(2018-TDMS011)。
文摘During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.
基金National Key R&D Program of China under Grant Nos.2023YFA1606400 and 2022YFA1602303National Natural Science Foundation of China under Grants Nos.12335007,12035001,11921006,12347106,12147101,and 12205340+1 种基金Gansu Natural Science Foundation under Grant No.22JR5RA123U.S.Department of Energy(DOE),Office of Science,under SciDAC-5(NUCLEI collaboration)。
文摘Over the last decade,nuclear theory has made dramatic progress in few-body and ab initio many-body calculations.These great advances stem from chiral efective feld theory(xEFT),which provides an efcient expansion and consistent treatment of nuclear forces as inputs of modern many-body calculations,among which the in-medium similarity renormalization group(IMSRG)and its variants play a vital role.On the other hand,signifcant eforts have been made to provide a unifed description of the structure,decay,and reactions of the nuclei as open quantum systems.While a fully comprehensive and microscopic model has yet to be realized,substantial progress over recent decades has enhanced our understanding of open quantum systems around the dripline,which are often characterized by exotic structures and decay modes.To study these interesting phenomena,Gamow coupled-channel(GCC)method,in which the open quantum nature of few-body valence nucleons coupled to a deformed core,has been developed.This review focuses on the developments of the advanced IMSRG and GCC and their applications to nuclear structure and reactions.
基金supported by the National Natural Science Foundation of China through the Project "Science Center for Luminescence from Molecular Aggregates(SCELMA)" (No.21788102)the Ministry of Science and Technology of China through the National Key R&D Plan (No.2017YFA0204501)supported by the National Natural Science Foundation of China (No.22003029)
文摘We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.
文摘Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and thermal diffusivity are derived.
基金supported by the National Natural Science Foundation of China (10872192)
文摘With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.
基金Supported by the Chinese National Science Foundation under Grant No.10874003 by Ministry of Science and Technology of China under Grant No.2006CB921300
文摘In the present paper, we study effect of the long-range Coulomb interaction on the thermodynamic propertiesof graphene by renormalization group methods.Our calculations show that both the specific heat and the magneticsusceptibility of the material behave differently from the Landau Fermi liquid.More precisely, we find that thesequantities are logarithmically suppressed with respect to its noninteracting counterpart when temperature is low.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11834005,and 11904145)the Program for Changjiang Scholars and Innovative Research Team in Universities,China(Grant No.IRT-16R35).
文摘We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.
文摘This paper presents the application of the renormalization group （RG） methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equations, and then obtain the approximate solutions by solving the corresponding RG equations. It shows that the approximate solutions obtained from the RG method are superior to those from the conventionally perturbation methods.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11834005,and 11904145)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35).
文摘We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.
基金Supported in part by BMBF under Grant No.05P2015–NUSTAR R&D)DFG and NSFC through Funds Provided to the SinoGerman CRC 110 “Symmetries and the Emergence of Structure in QCD”+2 种基金National Natural Science Foundation of China under Grant No.11621131001,DFG Grant No.TRR110the Georgian Shota Rustaveli National Science Foundation(grant FR/417/6-100/14)the CAS President’s International Fellowship Initiative(PIFI)under Grant No.2017VMA0025
文摘The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced.A system of integro-differential equations for the cutoff-dependent potential is obtained.As an illustration,a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained.The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.
文摘We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R<sub>1</sub> and R<sub>2 </sub>of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.
基金supported by National Natural Science Foundation of China(Grant No.12288201)。
文摘We focus on the interpretability of deep neural networks(DNNs).DNNs are currently the most widely used models in the field of artificial intelligence.However,they have been considered to lack interpretability.The most significant advantage of DNNs is that they can extract the features from big data effectively.The renormalization group(RG)is a kind of method in statistical physics.Physics research has shown that this method can effectively derive the macroscopic features from the microscopic characteristics of statistical physical systems.The coarse-graining procedure of the real-space RG is quite similar to the calculation in the forward propagation of DNNs.Inspired by this viewpoint,we consider establishing a corresponding relationship between the training process of the DNNs and RG.We propose a new framework to study the interpretability of DNNs using the RG method,and our main results are as follows:(1)Considering the input data and the main features extracted by a DNN as two statistical physical systems,we propose a rigorous correspondence relationship between the RG of input data and the training process of the DNN.Therefore,the DNN can be seen as a system artificially defined by its parameters,which carries out a non-canonical RG process on the data.(2)We prove that,when the input dataset is the one-dimensional Ising model,after the training process of the fully connected DNN,the limit of the coupling constant in the partition function of the network output is the same as the stable fixed point of the coupling constant calculated by the real-space RG on the input dataset.This shows that the ability of feature extraction of the DNN originates from the equivalence between their training process and the canonical RG.Also,both the DNN and RG extract the same macroscopic features from the data,which are the contents actually learned by the DNN.
基金supported by National Natural Science Foundation of China(Grants Nos.11934020 and 12274380)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302402)+1 种基金supported by the“Qiushi Academic-Dongliang”Talent Cultivation Program of Renmin University of China(Grant No.RUC24QSDL040)Computational resources were provided by Physical Laboratory of High Performance Computing in Renmin University of China.
文摘In this study,we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials.This ab initio many-body computational toolkit,termed Zen,utilizes the VASP and Quantum ESPRESSO codes to perform first-principles calculations and generate band structures for realistic materials.The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers:the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperatures.To validate the performance of this toolkit,we examine three representative cases:correlated metal SrVO_(3),unconventional superconductor La_(3)Ni_(2)O_(7),and Mott insulator MnO.The calculated results exhibit excellent agreement with previously available experimental and theoretical findings.Thus,it is suggested that the Zen toolkit is proficient in accurately describing the electronic structures of d-electron correlated materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.12374042,and 11904155)the Guangdong Science and Technology Department(Grant No.2022A1515011948)the Shenzhen Science and Technology Program(Grant No.KQTD20200820113010023).
文摘Understanding the formation of novel pair density waves(PDWs)in strongly correlated electronic systems remains extremely challenging.Recent mean-field studies suggest that PDW phases may arise in strong-coupling multiband superconductors by the quantum geometric properties of paired electrons.However,scrutiny through sophisticated many-body calculations has been lacking.Employing large-scale density matrix renormalization group calculations,we obtain in the strong-coupling regime phase diagram as a function of doping concentration and a tuning interaction parameter for a simple two-orbital model that incorporates quantum geometric effects.The phase diagram reveals a robust PDW phase spanning a broad range of parameters,characterized by a Luttinger parameter K_(sc)~0.3 and the absence of coexisting competing spin or charge density wave orders.The observed pairing field configuration aligns with the phenomenological understanding that quantum geometry can promote PDW formation.Our study provides the most compelling numerical evidence to date for quantum-geometry-facilitated intrinsic PDW order in strongly correlated systems,paving the way for further exploration of novel PDW orders and quantum geometric effects in such systems.
基金NSFC grant(Nos.11771177,12171197)China Auto-mobile Industry Innovation and Development Joint Fund(No.U1664257)Program for Changbaishan Scholars of Jilin Province and Science and Technology Development Project of Jilin Province(No.YDZJ202101ZYTS141,20190201132JC).
文摘In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any order.2)We will refer that the RG procedure can,in fact,be used to get the normal form of differential dynamical systems.3)We will also present the approximating center manifolds of the perturbed systems,and investigate the long time asymptotic behavior by means of RG formula.
基金We thank Shuai Yin and Baoquan Feng for their helpful discussions. This work was supported by the National Natural Science foundation of PRC （Grants Nos. 10625420 and 11575297） and FRFCUC.
文摘We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.
基金the National Natural Science Foundation of China(Grant Nos.11874421,and 11774422)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.18XNLG11)。
文摘A magnetic impurity embedded in a Fermi sea is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale TK,the Kondo temperature,through the mechanism of the Kondo effect.We have reinvestigated the Kondo singlet by means of the newly developed natural orbitals renormalization group(NORG)method.We find that,in the framework of natural orbitals formalism,the Kondo screening mechanism becomes transparent and simple,while the intrinsic structure of a Kondo singlet is clearly resolved.For a single impurity Kondo system in whichever case of either finite size or thermodynamic limit,there exists a single active natural orbital that screens the magnetic impurity dominantly.In the perspective of entanglement,the magnetic impurity is entangled dominantly with the active natural orbital,i.e.,the subsystem formed by the active natural orbital and the magnetic impurity basically disentangles from the remaining system.We have also studied the structures of the active natural orbital respectively projected into real space and momentum space.Moreover,the dynamical properties,represented by one-particle Green’s functions defined at the active natural orbital,are obtained by the correction vector method.Meanwhile,the well-known Kondo resonance is clearly observed in the spectral function at the active natural orbital.To realize the thermodynamic limit,the Wilson chains with the numerical renormalization group approach are employed.
