Characterizing the many-body localization transition by the dynamics of diagonal entropy

Zheng-Hang Sun,Jian Cui,Heng Fan

doi:10.1103/physrevresearch.2.013163

Abstract

The authors present a method of charactering many-body localization transition via the quench dynamics of diagonal entropy, as an experimentally feasible quantity. The critical point of many-body localization transition can be efficiently detected. The adopted scaling ansatz respects the Harris-Luck bound, and the scaling exponent can provide information for the universality class of many-body localization transition.

Highlights

Whether a strongly correlated many-body system thermalizes over time is an intriguing question
Since the nonequilibrium properties of quantum systems are naturally available in quantum simulations, considerable attention has been attracted by the intense debate of many-body localization (MBL) from the dynamical perspectives, involving the many-body mobility edge [27,28] and MBL transition [29]
The properties of eigenstates only give the lower bound of critical point Wc ∼ 3.7–3.9, while the quench dynamics shows that the signatures of thermalization and MBL appear when W ∼ 4 and W ∼ 6, respectively, indicating that the range of critical strength is Wc ∈ [4, 6]

Summary

INTRODUCTION

Whether a strongly correlated many-body system thermalizes over time is an intriguing question. We study the DE of quenched states at time t = 300 and apply data collapse to obtain the critical strength Wc of quasiperiodic field and the corresponding scaling exponent ν. This treatment will be repeated at different times t. The properties of eigenstates only give the lower bound of critical point Wc ∼ 3.7–3.9, while the quench dynamics shows that the signatures of thermalization and MBL appear when W ∼ 4 and W ∼ 6, respectively, indicating that the range of critical strength is Wc ∈ [4, 6] (note a factor 2 applies as a result of a different definition of the spin matrices). The critical point can be accurately obtained by the data collapse of DE

Hamiltonian

The scaling exponents

SUMMARY AND DISCUSSION