Level spacing distribution of localized phases induced by quasiperiodic potentials

Abstract

Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized phase. Here we analytically obtain the level spacing distribution of the quasiperiodic localized phase, and find that it deviates from Poisson statistics. Moreover, based on this level statistics, we derive the ratio of adjacent gaps and find that for a single sample, it is a $\delta$ function, which is in excellent agreement with numerical studies. Additionally, unlike disordered systems, in quasiperiodic systems, there are variations in the level spacing distribution across different regions of the spectrum, and increasing the size and increasing the sample are non-equivalent. Our findings carry significant implications for the reevaluation of level statistics in quasiperiodic systems and a profound understanding of the distinct effects of quasiperiodic potentials and disorder induced localization.

References in corpus (20)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• Spectral signatures of many-body localization with interacting photons
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Exact new mobility edges between critical and localized states
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Drive Induced Delocalization in Aubry-André Model
• Fermionic many-body localization for random and quasiperiodic systems in the presence of short- and long-range interactions
• Quantum phase with coexisting localized, extended, and critical zones
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Quasiperiodicity, band topology, and moiré graphene
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• From topological phase to Anderson localization in a two-dimensional quasiperiodic system
• Dimensional reduction from magnetic field in moiré superlattices