Localization challenges quantum chaos in the finite two-dimensional Anderson model

Abstract

It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here we numerically study the quantum-chaos to localization transition in the finite 2D Anderson model using standard indicators used in the modern literature such as the level spacing ratio, spectral form factor, variances of observable matrix elements, participation entropy and the eigenstate entanglement entropy. We show that many features of these indicators may indicate emergence of robust single-particle quantum chaos at weak disorder. However, we argue that a careful numerical analysis is consistent with the single-parameter scaling theory and predicts the breakdown of quantum chaos at any nonzero disorder value in the thermodynamic limit. Among the hallmarks of this breakdown are the universal behavior of the spectral form factor at weak disorder, and the universal scaling of various indicators as a function of the parameter $u={\left(W\ln V\right)}^{-1}$ where $W$ is the disorder strength and $V$ is the number of lattice sites.

References in corpus (15)

• Thermalization and its mechanism for generic isolated quantum systems
• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Breakdown of thermalization in finite one-dimensional systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Can we study the many-body localisation transition?
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Is there slow particle transport in the MBL phase?
• Critical properties of the Anderson localization transition and the high dimensional limit
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Unbinding transition in semi-infinite two-dimensional localized systems
• Restoring ergodicity in a strongly disordered interacting chain
• Tight-binding billiards

Cited by in corpus (16)

• Many-Body Localization in the Age of Classical Computing
• Scale-invariant critical dynamics at eigenstate transitions
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Long-range spectral statistics of the Rosenzweig-Porter model
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Single-quasiparticle eigenstate thermalization
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Anderson localization induced by structural disorder
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Controlling nonergodicity in quantum many-body systems by reinforcement learning
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Scaling theory of fading ergodicity
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• Rationally independent free fermions with local hopping
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Localization transitions in quadratic systems without quantum chaos