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Localization and Dynamics in One-Dimensional and Two-Dimensional Gaussian Disordered Quantum Spin Systems

Dongyan Guo, Taotao Hu, Jiameng Hong

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.2139/ssrn.5131958

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Localization and Dynamics in One-dimensional and Two-dimensional Gaussian Disordered Quantum Spin Systems

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This paper introduces Gaussian disorder, characterized by two parameters:the expected value and the standard deviation.Studying this type of disorder enhances our understanding of how many-body localization (MBL) transition is influenced by the central value and breadth of disorder.We apply Gaussian disorder to a one-dimensional spin-1/2 chain to reveal its features.Our findings indicate that the crucial parameter driving localization transitions is the standard deviation; as it increases, the system transitions from the ergodic phase to the localized phase, while the expected value has no effect,so the critical factor influencing MBL transition is the breadth of disorder rather than its central value.We then explore Gaussian disorder in two system-environment models (hereafter referred to as the sye-env models, consisting of ladder configuration and staggered configuration),analyzing the mutual influence when they are coupled.We extensively explore the impacts brought about by system disorder,environment disorder,initial state,and the strength of the sys-env interaction.Finally,for theses two different models,we consider the system and environment as a whole,studying how the localization properties of the entire system are influenced by the disorder strength of each chain and the interaction strength between the two chains.In the ladder configuration, we observe a strong dependence on the initial state,which can lead to either the loss or retention of information,whereas no such dependence on the initial state is found in the staggered configuration.We emphasize that when using dynamic indicators to analyze system characteristics, it is essential to consider the influence of different initial states,as this may lead to significant differences under certain structural conditions,and not all initial states can accurately reflect the localization properties of the many-body system.

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Bulletin of the American Physical Society•Mar 17, 2016•0 citations
This paper introduces Gaussian disorder, characterized by two parameters:the expected value and the standard deviation.Studying this type of disorder enhances our understanding of how many-body localization (MBL) transition is influenced by the central value and breadth of disorder.We apply Gaussian disorder to a one-dimensional spin-1/2 chain to reveal its features.Our findings indicate that the crucial parameter driving localization transitions is the standard deviation; as it increases, the system transitions from the ergodic phase to the localized phase, while the expected value has no effect,so the critical factor influencing MBL transition is the breadth of disorder rather than its central value.We then explore Gaussian disorder in two system-environment models (hereafter referred to as the sye-env models, consisting of ladder configuration and staggered configuration),analyzing the mutual influence when they are coupled.We extensively explore the impacts brought about by system disorder,environment disorder,initial state,and the strength of the sys-env interaction.Finally,for theses two different models,we consider the system and environment as a whole,studying how the localization properties of the entire system are influenced by the disorder strength of each chain and the interaction strength between the two chains.In the ladder configuration, we observe a strong dependence on the initial state,which can lead to either the loss or retention of information,whereas no such dependence on the initial state is found in the staggered configuration.We emphasize that when using dynamic indicators to analyze system characteristics, it is essential to consider the influence of different initial states,as this may lead to significant differences under certain structural conditions,and not all initial states can accurately reflect the localization properties of the many-body system.
We propose a Gaussian disorder to study many-body localization (MBL) in one-dimensional quantum system and coupled system-environment models. Unlike uniform disorder, Gaussian disorder is controlled by the standard deviation σ (driving MBL transitions) and the mean μ (causing global energy shifts). By calculating the von Neumann entropy, mean gap ratio, and dynamical indicators, we elucidate the ergodic-to-MBL transition as σ , with Gaussian disorder exhibiting more pronounced finite-size critical point drift effects compared to conventional random disorder. Through finite-size scaling analysis, it shows that there are no significant differences between the two disorder types at our assumed system sizes. We construct two system-environment coupling configurations (ladder and staggered), showing that under weak coupling, the system and environment evolve independently, whereas strong coupling induces cooperative localization. The ladder configuration shows a strong dependence on the initial state, which may lead to either the loss or retention of information, while no such dependence is observed in the staggered configuration. This can be explained by the changes in energy density of the initial state caused by variations in different model structures. When treating the system-environment as a unified two-dimensional ladder, asymmetric disorder on the two chains can drive a global MBL phase transition, with slightly different behaviors compared to symmetric disorder. Additionally, we emphasize the necessity of correctly selecting the initial state when characterizing the phase transition through dynamic indicators.
We investigate the dynamics of the random one-dimensional spin-1/2 quantum isotropic XYXYXY model in high-temperature limit by the recurrence relations method. Both the time-dependent transverse autocorrelation function and the corresponding spectral density are calculated for the cases that the exchange couplings between spins or transverse fields satisfy the double-Gaussian distribution. It is found that when the value of ${\ensuremath{\sigma}}_{J}$ (standard deviation of random exchange coupling) or ${\ensuremath{\sigma}}_{B}$ (standard deviation of random external magnetic field) is small, the dynamics of the system undergoes a crossover between a central-peak behavior and a collective-mode one. However, when ${\ensuremath{\sigma}}_{J}$ or ${\ensuremath{\sigma}}_{B}$ is large enough, the crossover vanishes, and the system shows the most disordered behavior or a central-peak behavior. We also investigate the cases that the couplings or fields satisfy the bimodal distribution and Gaussian distribution, which are the two special cases of double-Gaussian distribution, and find that the dynamics of the system is similar to that of the one-dimensional transverse Ising system.