Imbalance for a family of one-dimensional incommensurate models with mobility edges

Abstract

In this paper, we look at four generalizations of the one dimensional Aubry-Andre-Harper (AAH) model which possess mobility edges. We map out a phase diagram in terms of population imbalance, and look at the system size dependence of the steady state imbalance. We find non-monotonic behaviour of imbalance with system parameters, which contradicts the idea that the relaxation of an initial imbalance is fixed only by the ratio of number of extended states to number of localized states. We propose that there exists dimensionless parameters, which depend on the fraction of single particle localized states, single particle extended states and the mean participation ratio of these states. These ingredients fully control the imbalance in the long time limit and we present numerical evidence of this claim. Among the four models considered, three of them have interesting duality relations and their location of mobility edges are known. One of the models (next nearest neighbour coupling) has no known duality but mobility edge exists and the model has been experimentally realized. Our findings are an important step forward to understanding non-equilibrium phenomena in a family of interesting models with incommensurate potentials.

13 pages, 2 tables, 10 figures

References in corpus (13)

• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
• Self-dual quasiperiodic systems with power-law hopping
• Anderson localization transitions with and without random potentials
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Non-Abelian gauge potential driven localization transition in quasiperiodic optical lattices

Cited by in corpus (4)

• Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
• The general approach to the critical phase with coupled quasiperiodic chains
• Exact mobility edges for 1D quasiperiodic models
• Strongly interacting bosons in 1D disordered lattice: phase coherence of distorted Mott phases