From ergodicity to Stark many-body localization in spin chains with single-ion anisotropy

TL;DR

This paper demonstrates that single-ion anisotropy can induce many-body localization in spin chains, even without disorder, by suppressing thermalization through local energetic constraints and resonances.

Contribution

It reveals that single-ion anisotropy alone can cause Stark many-body localization in spin chains, expanding understanding of localization mechanisms beyond disorder.

Findings

Magnetic field gradient suppresses thermalization, leading to SMBL.

Single-ion anisotropy alone can prevent thermalization.

Competition between field and anisotropy can induce delocalization.

Abstract

The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with $S\geq 1/2$ within the Majumdar-Ghosh model, incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in $S=1/2$ chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized $S\geq 1/2$ systems.