Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We ...Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.展开更多
Ising superconductivity has garnered much attention in recent years due to its extremely high in-plane upper critical field (B_(c2)).Here,we fabricated 14 multilayer Pb_(1-x)Bi_(x) (0%≤x≤40%) thin films on Si (111)-...Ising superconductivity has garnered much attention in recent years due to its extremely high in-plane upper critical field (B_(c2)).Here,we fabricated 14 multilayer Pb_(1-x)Bi_(x) (0%≤x≤40%) thin films on Si (111)-7×7 reconstructed surface by molecular beam epitaxy.Large B_(c2) beyond the Pauli limit is observed in all the Pb_(1-x)Bi_(x) films,indicating that they may exhibit characteristics of Ising superconductivity.Moreover,the introduction of Bi doping can significantly enhance and effectively tune the in-plane B_(c2) of Pb_(1-x)Bi_(x) films,which will help us better understand Ising superconductivity and provide a new platform for the development of tunable Ising superconductors.展开更多
Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scali...Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.展开更多
Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwid...Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwidth.Recently,there has been growing interest in using photonic platforms to accelerate the optimization of Ising models,paving the way for the development of ultrafast hardware in machine learning.However,these proposed systems face challenges in simultaneously achieving high spin scalability,encoding flexibility,and low system complexity.We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation.We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems.The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes.Furthermore,we demonstrate the feasibility of scaling the system to 256 spins.This approach verifies the viability of performing Ising simulations in the wavelength dimension,offering substantial advantages in scalability.These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.展开更多
本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能...本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能的顶点算子代数结构。In this paper, we mainly study the vertex operator algebra generated by two pairs of Ising vectors in the moonshine type vertex operator algebra. These two pairs of Ising vectors each generate one 3A algebra, and the intersection of the two generated 3A algebras contains a subvertex operator subalgebra that is isomorphic to L(4/5, 0)⊕L(4/5, 3). We have shown that there are three possible structures of vertex operators algebraic.展开更多
Ising superconductivity, induced by the strong spin–orbit coupling(SOC) and inversion symmetry breaking, can lead to the in-plane upper critical field exceeding the Pauli limit and hold significant potential for adva...Ising superconductivity, induced by the strong spin–orbit coupling(SOC) and inversion symmetry breaking, can lead to the in-plane upper critical field exceeding the Pauli limit and hold significant potential for advancing the study of topological superconductivity. However, the enhancement of Ising superconductivity is still a challenging problem, important for engineering Majorana fermions and exploring topological quantum computing. In this study, we investigated the superconducting properties of a series of van der Waals NbSe_(2-x)Te_(x) nanosheets. The Ising superconductivity in NbSe_(2-x)Te_(x) nanosheets can be significantly enhanced by the substitution of Te, an element with strong SOC. The fitted in-plane upper critical field of Nb Se_(1.5)Te_(0.5) nanosheets at absolute zero temperature reaches up to 3.2 times the Pauli limit. Angular dependence of magnetoresistance measurements reveals a distinct two-fold rotational symmetry in the superconducting transition region, highlighting the role of strong SOC. In addition, the fitting results of the Berezinskii–Kosterlitz–Thouless(BKT) transition and the two-dimensional(2D) Tinkham formula provide strong evidence for 2D superconductivity. These findings offer new perspectives for the design and modulation of the Ising superconducting state and pave the way for their potential applications in topological superconductivity and quantum technologies.展开更多
Systems with quenched disorder possess complex energy landscapes that are challenging to explore under conventional Monte Carlo methods.In this work,we implement an efficient entropy sampling scheme for accurate compu...Systems with quenched disorder possess complex energy landscapes that are challenging to explore under conventional Monte Carlo methods.In this work,we implement an efficient entropy sampling scheme for accurate computation of the entropy function in low-energy regions.The method is applied to the two-dimensional±J random-bond Ising model,where frustration is controlled by the fraction p of ferromagnetic bonds.We investigate the low-temperature paramagnetic–ferromagnetic phase boundary below the multicritical point at T_(N)=0.9530(4),P_(N)=0.89078(8),as well as the zerotemperature ferromagnetic–spin-glass transition.Finite-size scaling analysis reveals that the phase boundary for T<T_(N) exhibits reentrant behavior.By analyzing the evolution of the magnetizationresolved density of states g(E,M)and ground-state spin configurations against increasing frustration,we provide strong evidence that the zero-temperature transition is a mixed-order.Finite-size scaling conducted on the spin-glass side supports the validity of β=0,whereβis the magnetization exponent,with a correlation length exponentν=1.50(8).Our results provide new insights into the nature of the ferromagnetic-to-spin-glass phase transition in an extensively degenerate ground state.展开更多
A uniform longitudinal field applied to the transverse Ising model(TIM)distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart.While the ground state of the latter shows no quantum pha...A uniform longitudinal field applied to the transverse Ising model(TIM)distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart.While the ground state of the latter shows no quantum phase transition(QPT),the ground state of the former exhibits rich phases:paramagnetic,antiferromagnetic,and possibly disordered phases.Although the first two are clearly identified,the existence of the disordered phase remains controversial.Here,we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction J,the transverse field hx and the longitudinal field h_(z),and uncover which patterns are responsible for these three competing energy scales,thereby determining the possible phases and the QPTs among them.The system size ranges from L=8 to 128 and the transverse field hx is fixed at 1.Under these parameters,our results show the existence of the disordered phase.For a small h_(z),the system transitions from a disordered phase to an antiferromagnetic phase as J increases.For a large h_(z),the system undergoes two phase transitions:from paramagnetic to disordered,and then to antiferromagnetic phase.These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.展开更多
We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the tran...We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.展开更多
基金supported by the National Natural Science Foundation of China Grant Nos.12450004,12274288the Innovation Program for Quantum Science and Technology Grant No.2021ZD0301900。
文摘Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12374196, 92165201, and 11634011)the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302800)+2 种基金the Chinese Academy of Sciences Project for Young Scientists in Basic Research (Grant No. YSBR-046)the Fundamental Research Funds for the Central Universities (Grant Nos. WK3510000006 and WK3430000003)Anhui Initiative in Quantum Information Technologies (Grant No. AHY170000)。
文摘Ising superconductivity has garnered much attention in recent years due to its extremely high in-plane upper critical field (B_(c2)).Here,we fabricated 14 multilayer Pb_(1-x)Bi_(x) (0%≤x≤40%) thin films on Si (111)-7×7 reconstructed surface by molecular beam epitaxy.Large B_(c2) beyond the Pauli limit is observed in all the Pb_(1-x)Bi_(x) films,indicating that they may exhibit characteristics of Ising superconductivity.Moreover,the introduction of Bi doping can significantly enhance and effectively tune the in-plane B_(c2) of Pb_(1-x)Bi_(x) films,which will help us better understand Ising superconductivity and provide a new platform for the development of tunable Ising superconductors.
基金supported by the National Natural Science Foundation of China(Grant No.12175316).
文摘Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB2804203)the National Natural Science Foundation of China(Grant No.U21A20511)the Knowledge Innovation Program of Wuhan-Basic Research(Grant No.2023010201010049).
文摘Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwidth.Recently,there has been growing interest in using photonic platforms to accelerate the optimization of Ising models,paving the way for the development of ultrafast hardware in machine learning.However,these proposed systems face challenges in simultaneously achieving high spin scalability,encoding flexibility,and low system complexity.We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation.We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems.The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes.Furthermore,we demonstrate the feasibility of scaling the system to 256 spins.This approach verifies the viability of performing Ising simulations in the wavelength dimension,offering substantial advantages in scalability.These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.
文摘本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能的顶点算子代数结构。In this paper, we mainly study the vertex operator algebra generated by two pairs of Ising vectors in the moonshine type vertex operator algebra. These two pairs of Ising vectors each generate one 3A algebra, and the intersection of the two generated 3A algebras contains a subvertex operator subalgebra that is isomorphic to L(4/5, 0)⊕L(4/5, 3). We have shown that there are three possible structures of vertex operators algebraic.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62488201 and 1240041502)the China Postdoctoral Science Foundation (Grant No. 2024T170990)+2 种基金the National Key R&D Program of China (Grant No. 2022YFA1204100)the Chinese Academy of Sciences (Grant No. XDB33030100)the Innovation Program of Quantum Science and Technology (Grant No. 2021ZD0302700)。
文摘Ising superconductivity, induced by the strong spin–orbit coupling(SOC) and inversion symmetry breaking, can lead to the in-plane upper critical field exceeding the Pauli limit and hold significant potential for advancing the study of topological superconductivity. However, the enhancement of Ising superconductivity is still a challenging problem, important for engineering Majorana fermions and exploring topological quantum computing. In this study, we investigated the superconducting properties of a series of van der Waals NbSe_(2-x)Te_(x) nanosheets. The Ising superconductivity in NbSe_(2-x)Te_(x) nanosheets can be significantly enhanced by the substitution of Te, an element with strong SOC. The fitted in-plane upper critical field of Nb Se_(1.5)Te_(0.5) nanosheets at absolute zero temperature reaches up to 3.2 times the Pauli limit. Angular dependence of magnetoresistance measurements reveals a distinct two-fold rotational symmetry in the superconducting transition region, highlighting the role of strong SOC. In addition, the fitting results of the Berezinskii–Kosterlitz–Thouless(BKT) transition and the two-dimensional(2D) Tinkham formula provide strong evidence for 2D superconductivity. These findings offer new perspectives for the design and modulation of the Ising superconducting state and pave the way for their potential applications in topological superconductivity and quantum technologies.
基金supported by NKRDPC-2022YFA1402802,NSFC-92165204the Research Grants Council of the HKSAR under Grant Nos.12304020 and 12301723+2 种基金Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices under Grant No.2022B1212010008Guangdong Fundamental Research Center for Magnetoelectric Physics under Grant No.2024B0303390001Guangdong Provincial Quantum Science Strategic Initiative under Grant No.GDZX2401010。
文摘Systems with quenched disorder possess complex energy landscapes that are challenging to explore under conventional Monte Carlo methods.In this work,we implement an efficient entropy sampling scheme for accurate computation of the entropy function in low-energy regions.The method is applied to the two-dimensional±J random-bond Ising model,where frustration is controlled by the fraction p of ferromagnetic bonds.We investigate the low-temperature paramagnetic–ferromagnetic phase boundary below the multicritical point at T_(N)=0.9530(4),P_(N)=0.89078(8),as well as the zerotemperature ferromagnetic–spin-glass transition.Finite-size scaling analysis reveals that the phase boundary for T<T_(N) exhibits reentrant behavior.By analyzing the evolution of the magnetizationresolved density of states g(E,M)and ground-state spin configurations against increasing frustration,we provide strong evidence that the zero-temperature transition is a mixed-order.Finite-size scaling conducted on the spin-glass side supports the validity of β=0,whereβis the magnetization exponent,with a correlation length exponentν=1.50(8).Our results provide new insights into the nature of the ferromagnetic-to-spin-glass phase transition in an extensively degenerate ground state.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFA1402704)the National Natural Science Foundation of China(Grant No.12247101)。
文摘A uniform longitudinal field applied to the transverse Ising model(TIM)distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart.While the ground state of the latter shows no quantum phase transition(QPT),the ground state of the former exhibits rich phases:paramagnetic,antiferromagnetic,and possibly disordered phases.Although the first two are clearly identified,the existence of the disordered phase remains controversial.Here,we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction J,the transverse field hx and the longitudinal field h_(z),and uncover which patterns are responsible for these three competing energy scales,thereby determining the possible phases and the QPTs among them.The system size ranges from L=8 to 128 and the transverse field hx is fixed at 1.Under these parameters,our results show the existence of the disordered phase.For a small h_(z),the system transitions from a disordered phase to an antiferromagnetic phase as J increases.For a large h_(z),the system undergoes two phase transitions:from paramagnetic to disordered,and then to antiferromagnetic phase.These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.
基金supported by the National Natural Science Foundation of China(Grant Nos.12475033,12135003,12174194,and 12405032)the National Key Research and Development Program of China(Grant No.2023YFE0109000)+1 种基金supported by the Fundamental Research Funds for the Central Universitiessupport from the China Postdoctoral Science Foundation(Grant No.2023M730299).
文摘We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.
基金Supported by the National Natural Science Foundation of China(11074184)the Foundation for University Key Young Teacher of Henan Province(2009GGJS-163)
