We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimen...We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.展开更多
We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which t...We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which the time evolution of the entanglement in momentum space can be investigated.We note that depending on the choice of Bogoliubov quasiparticles,the expressions of wavefunctions,which describe time-evolved paired states,can take different forms.The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed,which generalizes the results of Dora et al(2016,Phys.Rev.Lett.117,010603).A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.展开更多
For most of the conventional crystals with low-index surfaces, the hopping between the nearest neighbor （1NN） crystal planes （CPs） is dominant and the ones from the nNN （2 〈 n 〈 ∞） CPs are relatively weak, co...For most of the conventional crystals with low-index surfaces, the hopping between the nearest neighbor （1NN） crystal planes （CPs） is dominant and the ones from the nNN （2 〈 n 〈 ∞） CPs are relatively weak, considered as small perturbations. The recent theoretical analysisIll has demonstrated the absence of surface states at the level of the hopping approximation between the INN CPs when the original infinite crystal has the geometric reflection symmetry （GRS） for each CP. Meanwhile, based on the perturbation theory, it has also been shown that small perturbations from the hopping between the nNN （2 〈 n 〈 ∞） CPs and surface relaxation have no impact on the above conclusion. However, for the crystals with strong intrinsic spin-orbit coupling （SOC）, the dominant terms of intrinsic SOC associate with two INN bond hoppings. Thus SOC will significantly contribute the hoppings from the INN and/or 2NN CPs except the ones within each CP. Here, we will study the effect of the hopping between the 2NN CPs on the surface states in model crystals with three different type structures （Type I： “……P-P-P-P……”, Type II： “……-P-Q-P-Q……” and Type III：“……P=Q-P=Q……” where P and Q indicate CPs and the signs “-” and “=” mark the distance between the INN CPs）. In terms of analytical and numerical calculations, we study the behavior of surface states in three types after the symmetric/asymmetric hopping from the 2NN CPs is added. We analytically prove that the symmetric hopping from the 2NN CPs cannot induce surface states in Type I when each CP has only one electron mode. The numerical calculations also provide strong support for the conclusion, even up to 5NN. However, in general, the coupling from the 2NN CPs （symmetric and asymmetric） is favorable to generate surface states except Type I with single electron mode only.展开更多
The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The...The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one-and twodimensional Gauss quadratures.Then lower order Gauss quadrature,which is generated from Lanczos iteration,can be applied to approximate the initial weighted summation.This framework fills the conceptual gap between FTLM and kernel polynomial method,and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.展开更多
The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderate...The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime.The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≤ L ≤ 4N to obtain the ground and low-lying eigenstates.Our numerical results show that breathing modes with N-body eigenenergy spacing of 2hω⊥,known to exist in strictly 2D system with zero-range(δ-function) interaction potential,may as well exist in quasi-2D system with finite-range Gaussian interaction potential.To gain an insight into the many-body states,the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates.In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N(N-1) with q=2,4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose–Laughlin like state.We further observe that the first breathing mode exhibits features similar to the Bose–Laughlin state in having eigenenergy,von Neumann entropy and internal structure independent of interaction for the three-boson system considered here.On the contrary,for eigenstates lying between the Bose–Laughlin like ground state and the first breathing mode,values of eigenenergy,von Neumann entropy and internal structure are found to vary with interaction.展开更多
Research on nickel-based superconductors has progressed from infinite-layer LaNiO_(2) to finite-layer La_(6)Ni_(5)O_(12),and most recently to the Ruddlesden-Popper phase La_(3)Ni_(2)O_(7),which was found to exhibit on...Research on nickel-based superconductors has progressed from infinite-layer LaNiO_(2) to finite-layer La_(6)Ni_(5)O_(12),and most recently to the Ruddlesden-Popper phase La_(3)Ni_(2)O_(7),which was found to exhibit onset of superconductivity at∼80K under a pressure of∼16 GPa.Using density functional calculations and multi-orbital,multi-atom cluster exact diagonalization that includes local exchange and Coulomb interactions,here we analyze the pressure dependent low-energy electronic states of the Ni_(2)O_(9) cluster,relevant for the bilayer phase of La_(3)Ni_(2)O_(7).We quantify the various possible spin states and the exchange and superexchange mechanisms of the Ni_(2)O_(9) cluster are quantified through the involvement of the Ni-3d_(3z^(2)−r^(2)) orbitals and the atomic Hund’s rule exchange,the apical bridging O-2pz orbitals,and the orbitals involved in the formation of local Zhang-Rice singlet like states.We find that the leading configurations contributing to the cluster ground-states both for nominal valence and also with local charge fluctuations,do not involve occupation of the apical oxygen;instead,they favor the formation of in-plane Zhang-Rice singlet-like states between an O ligand hole and the Ni 3d_(z^(2)−y^(2)) orbital.We also highlight two possible charge and spin ordered states suggested by our cluster results,that are nearly degenerate at all relevant pressures within our modeling.展开更多
This paper explores the numerical study of quantum many-body systems with an emphasis on exact diagonalization techniques.The complexity of strongly correlated systems,often governed by large Hilbert spaces,presents s...This paper explores the numerical study of quantum many-body systems with an emphasis on exact diagonalization techniques.The complexity of strongly correlated systems,often governed by large Hilbert spaces,presents significant computational challenges,making exact solutions d ifficult.In this work,we examine methods to simplify these systems by leveraging techniques such as the Schrieffer-Wolff transformation,which decouples high-energy and low-energy states,and the use of symmetry operators to block-diagonalize Hamiltonians and so on.These approaches are demonstrated with examples such as the hydrogen atom and a lambda system.The second part of the paper focuses on specific case studies,including a one-dimensional spin model and Bose-Hubbard model.The latter is crucial for understanding the behavior of interacting bosons in lattice systems and phenomena such as the superfluid-Mott i nsulator t ransition.We present a detailed investigation of t he phase diagram f or t he onedimensional Bose-Hubbard model using both exact diagonalization and mean field theory,providing insights into its quantum phase transitions.This study underscores the potential of exact diagonalization in quantum simulations and highlights its relevance for experimental setups involving trapped ions and superconducting qubits.展开更多
By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation,we study the dynamical properties of the S=1 antiferromagnetic Heisenberg chain with different strengths of...By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation,we study the dynamical properties of the S=1 antiferromagnetic Heisenberg chain with different strengths of bond disorder.In the weak disorder region,we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode.As the disorder increases,the average Haldane gap closes at δ_(∆)~0.5 with more and more low-energy excitations coming out.After the critical disorder strength δ_(C)~1,the system reaches a random-singlet phase with prominent sharp peak atω=0 and broad continuum atω>0 of the dynamic spin structure factor.In addition,we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between.These“spins”can form the weakly coupled longrange singlets due to quantum fluctuation which contribute to the sharp peak atω=0.展开更多
A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoret...A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoretical analysis demonstrates that a combined dual-frequency laser beam with this setup strictly meets orthogonal linear relation. The experimental results show that compared with the conventional setup, the ellipticity and nonorthogonality of the combined dual-frequency laser beam are significantly reduced.展开更多
基金supported by the National Key Projects for Research and Development of China(Grant Nos.2021YFA1400400 and 2024YFA1408104)the National Natural Science Foundation of China(Grant Nos.12434005,12374137,and 92165205).
文摘We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.
基金H.L.acknowledges support from the National Natural Science Foundation of China(Grant Nos.11474136,11874187 and 12047501).
文摘We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which the time evolution of the entanglement in momentum space can be investigated.We note that depending on the choice of Bogoliubov quasiparticles,the expressions of wavefunctions,which describe time-evolved paired states,can take different forms.The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed,which generalizes the results of Dora et al(2016,Phys.Rev.Lett.117,010603).A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.
基金supported by the National Natural Science Foundation of China(Grant No.11447601)the National Basic Research Program of China(Grant No.2011CB921803)
文摘For most of the conventional crystals with low-index surfaces, the hopping between the nearest neighbor （1NN） crystal planes （CPs） is dominant and the ones from the nNN （2 〈 n 〈 ∞） CPs are relatively weak, considered as small perturbations. The recent theoretical analysisIll has demonstrated the absence of surface states at the level of the hopping approximation between the INN CPs when the original infinite crystal has the geometric reflection symmetry （GRS） for each CP. Meanwhile, based on the perturbation theory, it has also been shown that small perturbations from the hopping between the nNN （2 〈 n 〈 ∞） CPs and surface relaxation have no impact on the above conclusion. However, for the crystals with strong intrinsic spin-orbit coupling （SOC）, the dominant terms of intrinsic SOC associate with two INN bond hoppings. Thus SOC will significantly contribute the hoppings from the INN and/or 2NN CPs except the ones within each CP. Here, we will study the effect of the hopping between the 2NN CPs on the surface states in model crystals with three different type structures （Type I： “……P-P-P-P……”, Type II： “……-P-Q-P-Q……” and Type III：“……P=Q-P=Q……” where P and Q indicate CPs and the signs “-” and “=” mark the distance between the INN CPs）. In terms of analytical and numerical calculations, we study the behavior of surface states in three types after the symmetric/asymmetric hopping from the 2NN CPs is added. We analytically prove that the symmetric hopping from the 2NN CPs cannot induce surface states in Type I when each CP has only one electron mode. The numerical calculations also provide strong support for the conclusion, even up to 5NN. However, in general, the coupling from the 2NN CPs （symmetric and asymmetric） is favorable to generate surface states except Type I with single electron mode only.
基金supported by the National Natural Science Foundation of China(Grant Nos.11734002 and U1930402)。
文摘The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one-and twodimensional Gauss quadratures.Then lower order Gauss quadrature,which is generated from Lanczos iteration,can be applied to approximate the initial weighted summation.This framework fills the conceptual gap between FTLM and kernel polynomial method,and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.
文摘The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime.The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≤ L ≤ 4N to obtain the ground and low-lying eigenstates.Our numerical results show that breathing modes with N-body eigenenergy spacing of 2hω⊥,known to exist in strictly 2D system with zero-range(δ-function) interaction potential,may as well exist in quasi-2D system with finite-range Gaussian interaction potential.To gain an insight into the many-body states,the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates.In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N(N-1) with q=2,4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose–Laughlin like state.We further observe that the first breathing mode exhibits features similar to the Bose–Laughlin state in having eigenenergy,von Neumann entropy and internal structure independent of interaction for the three-boson system considered here.On the contrary,for eigenstates lying between the Bose–Laughlin like ground state and the first breathing mode,values of eigenenergy,von Neumann entropy and internal structure are found to vary with interaction.
基金the support of the National Natural Science Foundation of China(Grant No.12174278)support from the National Natural Science Foundation of China(Grant No.12422407)+3 种基金the Startup Funding from Soochow Universitythe Priority Academic Program Development of Jiangsu Higher Education Institutionssupported by the Quantum Matter Institute(QMI)at the University of British Columbiathe Natural Sciences and Engineering Research Council of Canada(NSERC).
文摘Research on nickel-based superconductors has progressed from infinite-layer LaNiO_(2) to finite-layer La_(6)Ni_(5)O_(12),and most recently to the Ruddlesden-Popper phase La_(3)Ni_(2)O_(7),which was found to exhibit onset of superconductivity at∼80K under a pressure of∼16 GPa.Using density functional calculations and multi-orbital,multi-atom cluster exact diagonalization that includes local exchange and Coulomb interactions,here we analyze the pressure dependent low-energy electronic states of the Ni_(2)O_(9) cluster,relevant for the bilayer phase of La_(3)Ni_(2)O_(7).We quantify the various possible spin states and the exchange and superexchange mechanisms of the Ni_(2)O_(9) cluster are quantified through the involvement of the Ni-3d_(3z^(2)−r^(2)) orbitals and the atomic Hund’s rule exchange,the apical bridging O-2pz orbitals,and the orbitals involved in the formation of local Zhang-Rice singlet like states.We find that the leading configurations contributing to the cluster ground-states both for nominal valence and also with local charge fluctuations,do not involve occupation of the apical oxygen;instead,they favor the formation of in-plane Zhang-Rice singlet-like states between an O ligand hole and the Ni 3d_(z^(2)−y^(2)) orbital.We also highlight two possible charge and spin ordered states suggested by our cluster results,that are nearly degenerate at all relevant pressures within our modeling.
文摘This paper explores the numerical study of quantum many-body systems with an emphasis on exact diagonalization techniques.The complexity of strongly correlated systems,often governed by large Hilbert spaces,presents significant computational challenges,making exact solutions d ifficult.In this work,we examine methods to simplify these systems by leveraging techniques such as the Schrieffer-Wolff transformation,which decouples high-energy and low-energy states,and the use of symmetry operators to block-diagonalize Hamiltonians and so on.These approaches are demonstrated with examples such as the hydrogen atom and a lambda system.The second part of the paper focuses on specific case studies,including a one-dimensional spin model and Bose-Hubbard model.The latter is crucial for understanding the behavior of interacting bosons in lattice systems and phenomena such as the superfluid-Mott i nsulator t ransition.We present a detailed investigation of t he phase diagram f or t he onedimensional Bose-Hubbard model using both exact diagonalization and mean field theory,providing insights into its quantum phase transitions.This study underscores the potential of exact diagonalization in quantum simulations and highlights its relevance for experimental setups involving trapped ions and superconducting qubits.
基金D.X.Y.,J.K.F,and J.H.H are supported by NKRDPC-2017YFA0206203,NKRDPC-2018YFA0306001,NSFC-11974432,GBABRF-2019A1515011337Shenzhen Institute for Quantum Science and Engineering,and Leading Talent Program of Guangdong Special Projects+1 种基金H.Q.W.is supported by NSFC-11804401the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(Grant No.2021qntd27).
文摘By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation,we study the dynamical properties of the S=1 antiferromagnetic Heisenberg chain with different strengths of bond disorder.In the weak disorder region,we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode.As the disorder increases,the average Haldane gap closes at δ_(∆)~0.5 with more and more low-energy excitations coming out.After the critical disorder strength δ_(C)~1,the system reaches a random-singlet phase with prominent sharp peak atω=0 and broad continuum atω>0 of the dynamic spin structure factor.In addition,we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between.These“spins”can form the weakly coupled longrange singlets due to quantum fluctuation which contribute to the sharp peak atω=0.
基金supported by the National Natural Science Foundation of China (No. 51305105)the China Postdoctoral Science Foundation (No. 2013M531024)the Fundamental Research Funds for the Central Universities (No. HIT. NSRIF. 2014008)
文摘A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoretical analysis demonstrates that a combined dual-frequency laser beam with this setup strictly meets orthogonal linear relation. The experimental results show that compared with the conventional setup, the ellipticity and nonorthogonality of the combined dual-frequency laser beam are significantly reduced.
