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
We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lin...We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories,enabling efficient simula-tion of dissipative quantum dynam-ics with effectively reduced quantum resources.Focusing on the one-di-mensional transverse-field Ising mod-el(TFIM),we simulate quench dynamics under both local and global Lindblad dissipation.The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function,and reveals their modulation by dissipation strength and system size.Notably,DQPTs are gradually suppressed under strong local dissipation,while they persist under strong global dissipation due to collective environmental effects.Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.展开更多
Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body systems.While they excel at analyzing static solutions,nonequilibrium processes,including critic...Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body systems.While they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural networks.To address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising model.Specifically,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength.The excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink numbers.Moreover,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the kinks.Finally,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.展开更多
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(Nos.22273122,T2350009)the Guangdong Provincial Natural Science Foundation(No.2024A1515011504)computational resources and services provided by the national supercomputer center in Guangzhou.
文摘We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories,enabling efficient simula-tion of dissipative quantum dynam-ics with effectively reduced quantum resources.Focusing on the one-di-mensional transverse-field Ising mod-el(TFIM),we simulate quench dynamics under both local and global Lindblad dissipation.The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function,and reveals their modulation by dissipation strength and system size.Notably,DQPTs are gradually suppressed under strong local dissipation,while they persist under strong global dissipation due to collective environmental effects.Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.
基金partially supported by the National Natural Science Foundation of China(Grants No.11875095 and 12175008).
文摘Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body systems.While they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural networks.To address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising model.Specifically,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength.The excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink numbers.Moreover,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the kinks.Finally,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.
