Statistically related many-body localization in the one-dimensional anyon Hubbard model

TL;DR

This paper investigates many-body localization in a one-dimensional disordered anyon-Hubbard model, revealing unique statistical effects on localization, entanglement, and energy level distributions, with implications for experimental detection.

Contribution

It introduces a detailed numerical analysis of MBL in the anyon-Hubbard model, highlighting the influence of anyon statistics on localization transitions and physical properties.

Findings

Logarithmic growth of entanglement entropy in MBL phase

Poisson-like energy level statistics in deep MBL phase

Non-monotonic dependence of physical quantities on anyon statistical angle

Abstract

Many-body localization (MBL) has been widely investigated for both fermions and bosons, it is, however, much less explored for anyons. Here we numerically calculate several physical characteristics related to MBL of a one-dimensional disordered anyon-Hubbard model in both localized and delocalized regions. We figure out a logarithmically slow growth of the half-chain entanglement entropy and an area-law rather than volume-law obedience for the highly excited eigenstates in the MBL phase. The adjacent energy level gap-ratio parameter is calculated and is found to exhibit a Poisson-like probability distribution in the deep MBL phase. By studying a hybridization parameter, we reveal an intriguing effect that the statistics can induce localization-delocalization transition. Several physical quantities, such as the half-chain entanglement, the adjacent energy level gap-ratio parameter, {\color{black} the long-time limit of the particle imbalance}, and the critical disorder strength, are shown to be non-monotonically dependent on the anyon statistical angle. Furthermore, a feasible scheme based on the spectroscopy of energy levels is proposed for the experimental observation of these statistically related properties.