# Exploring many body localization and thermalization using semiclassical method

## TL;DR

This paper evaluates the Discrete Truncated Wigner Approximation (DTWA) for studying many-body localization and thermalization, showing it captures key dynamical features in a 1D spin chain and could be useful for complex quantum systems.

## Contribution

The study demonstrates that DTWA can effectively reproduce dynamical signatures of MBL and thermal phases, especially at short times, and extends its potential use to higher-dimensional and long-range interacting systems.

## Key findings

- DTWA accurately reproduces dynamical signatures in both phases.
- DTWA captures logarithmic entanglement growth in MBL.
- Good agreement with exact solutions at short times.

## Abstract

The Discrete Truncated Wigner Approximation (DTWA) is a semi-classical phase space method useful for the exploration of Many-body quantum dynamics. In this work we investigate Many-Body Localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a 1D random field Heisenberg spin chain with short range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long range interactions and/or systems in higher dimensions.