Robust non-ergodicity of ground state in the $\beta$ ensemble

Abstract

In various chaotic quantum many-body systems, the ground states show non-trivial athermal behavior despite the bulk states exhibiting thermalization. Such athermal states play a crucial role in quantum information theory and its applications. Moreover, any generic quantum many-body system in the Krylov basis is represented by a tridiagonal Lanczos Hamiltonian, which is analogous to the matrices from the $\beta$ ensemble, a well-studied random matrix model with level repulsion tunable via the parameter $\beta$. Motivated by this, here we focus on the localization properties of the ground and anti-ground states of the $\beta$ ensemble. Both analytically and numerically, we show that both the edge states demonstrate non-ergodic (fractal) properties for $\beta \sim \mathcal{O}(1)$ while the typical bulk states are ergodic. Surprisingly, the fractal dimension of the edge states remain three time smaller than that of the bulk states irrespective of the global phase of the $\beta$ ensemble. In addition to the fractal dimensions, we also consider the distribution of the localization centers of the spectral edge states, their mutual separation, as well as the spatial and correlation properties of the first excited states.

arXiv comment4 figures in main text, 2 figures in appendix

References in corpus (77)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Entanglement in quantum critical phenomena
• Localization of interacting fermions at high temperature
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum Phase Transitions and Bipartite Entanglement
• Matrix Models for Beta Ensembles
• A Universal Operator Growth Hypothesis
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Multifractal Scalings across the Many-Body Localization Transition
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• One-dimensional quasicrystals with power-law hopping
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Thermal Fluctuations in Quantized Chaotic Systems
• A random matrix model with localization and ergodic transitions
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Many-body mobility edge in a mean-field quantum spin glass
• Correlation-induced localization
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Universal behavior beyond multifractality in quantum many-body systems
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Extended nonergodic states in disordered many-body quantum systems
• Return probability for the Anderson model on the random regular graph
• Delocalized Glassy Dynamics and Many Body Localization
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Classical Representation of the 1D Anderson Model
• Eigenfunction distribution for the Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Universal eigenstate entanglement of chaotic local Hamiltonians
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Non-Ergodic Delocalization in the Rosenzweig-Porter Model
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Large deviations of the maximal eigenvalue of random matrices
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Critical quantum chaos and the one dimensional Harper model
• Drive Induced Delocalization in Aubry-André Model
• Localization by bichromatic potentials versus Anderson localization
• Multifractal metal in a disordered Josephson Junction Array
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Quantum phase with coexisting localized, extended, and critical zones
• Emergent fractal phase in energy stratified random models
• Non-ergodic delocalized phase with Poisson level statistics
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• The right tail exponent of the Tracy-Widom-beta distribution
• Calculation of multifractal dimensions in spin chains
• Spectral density asymptotics for Gaussian and Laguerre $\beta$-ensembles in the exponentially small region
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Recursion for the smallest eigenvalue density of $\beta$-Wishart-Laguerre ensemble
• Random Cantor sets and mini-bands in local spectrum of quantum systems
• Tracy-Widom at high temperature
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Optimal soft edge scaling variables for the Gaussian and Laguerre even $\beta$ ensembles
• Chaos due to symmetry-breaking in deformed Poisson ensemble
• Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Transport in deformed centrosymmetric networks
• On statistical models on super trees
• Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
• Ground-state energy distribution of disordered many-body quantum systems

Cited by in corpus (9)

• Krylov fractality and complexity in generic random matrix ensembles
• Proposal for many-body quantum chaos detection
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Emergent multifractality in power-law decaying eigenstates
• Spectral form factor and energy correlations in banded random matrices
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Identifying mobility edge from finite temperature spectral form factor