Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: logarithmic multifractality and critical localization

• URL: http://arxiv.org/abs/2405.10975v1
• Date: Sun, 12 May 2024 12:55:28 GMT
• Title: Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: logarithmic multifractality and critical localization
• Authors: Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemarié,
• Abstract summary: This paper investigates two random matrix ensembles tailored to capture the critical behavior of the Anderson transition in infinite dimension. Our study unveils two types of critical behaviors: logarithmic multifractality and critical localization. Our findings enable broad applicability to systems with pronounced finite-size effects and slow dynamics.
• Score: 0.6374763930914524
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates two random matrix ensembles tailored to capture the critical behavior of the Anderson transition in infinite dimension, employing both analytical techniques and extensive numerical simulations. Our study unveils two types of critical behaviors: logarithmic multifractality and critical localization. In contrast to conventional multifractality, the novel logarithmic multifractality features eigenstate moments scaling algebraically with the logarithm of the system size. Critical localization, characterized by eigenstate moments of order $q>1/2$ converging to a finite value indicating localization, exhibits characteristic logarithmic finite-size or time effects, consistent with the critical behavior observed in random regular and Erd\"os-R\'enyi graphs of effective infinite dimensionality. Using perturbative methods, we establish the existence of logarithmic multifractality and critical localization in our models. Furthermore, we explore the emergence of novel scaling behaviors in the time dynamics and spatial correlation functions. Our models provide a valuable framework for studying infinite-dimensional quantum disordered systems, and the universality of our findings enables broad applicability to systems with pronounced finite-size effects and slow dynamics, including the contentious many-body localization transition, akin to the Anderson transition in infinite dimension.

Related papers

• Quantum logarithmic multifractality [0.6963971634605796]
  This work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing the Anderson transition. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition.
  arXiv  Detail & Related papers  (2023-12-29T05:56:52Z)
• Critical dynamics of long-range quantum disordered systems [0.3007949058551534]
  Long-range hopping in quantum disordered systems can yield quantum multifractality. We propose a model of wave packet expansion in long-range hopping systems. Our findings are of considerable interest towards applications in the fields of many-body localization and Anderson localization on random graphs.
  arXiv  Detail & Related papers  (2023-07-03T13:25:54Z)
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain [0.0]
  We explore the quantum phase transition of the one-dimensional long-range transverse-field Ising model. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. We successfully determine the universality boundary between the latter two as $sigma = 7/4$ based on the dynamical exponent.
  arXiv  Detail & Related papers  (2023-05-23T14:46:16Z)
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits [0.0]
  We identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. We show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic, sparse circuits.
  arXiv  Detail & Related papers  (2023-04-19T17:37:10Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations [0.0]
  The quantum-critical properties of the transverse-field Ising model are investigated by means of quantum Monte Carlo. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range universality classes.
  arXiv  Detail & Related papers  (2021-03-17T07:00:29Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.