Universal properties of single particle excitations across the many-body localization transition

Abstract

Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $\nu$ with which the correlation length $\xi$ diverges at the transition point $W_c$, $\xi \sim |W-W_c{|}^{-\nu }$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound $\nu \ge 2/d$ where $d$ is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level-spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion.

15 pages, 11 figs

References in corpus (24)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Avalanches and many-body resonances in many-body localized systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• How a small quantum bath can thermalize long localized chains
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Renormalization-group study of the many-body localization transition in one dimension
• Critical behavior at Mott-Anderson transition: a TMT-DMFT perspective
• Anderson localization transitions with and without random potentials
• Critical properties of the Anderson localization transition and the high dimensional limit
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Many-body localization near the critical point
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Average Density of States in Disordered Graphene systems
• Stability of many-body localization in Floquet systems
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• Detecting delocalization-localization transitions from full density distributions
• Scaling up the Anderson transition in random-regular graphs
• Mobility edge in long-range interacting many-body localized systems
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• Dynamics of Many-Body Delocalization in the Time-dependent Hartree-Fock Approximation
• Initial State Dependent Dynamics Across Many-body Localization Transition

Cited by in corpus (1)

• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry