Many-body localization in the random-field Heisenberg chain with Dzyaloshinskii-Moriya interaction

¹ School of Physics, Beijing Institute of Technology - Beijing 100081, China
² Center for Quantum Technology Research, School of Physics, Beijing Institute of Technology - Beijing 100081, China
³ Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology - Beijing 100081, China

^(a) E-mail: 55824644@qq.com; caoye05@163.com (corresponding author)
^(b) E-mail: wunwyz@gmail.com

Received: 8 January 2023
Accepted: 7 February 2023

Abstract

We study the one-dimensional spin-1/2 Heisenberg chain with Dzyaloshinskii-Moriya interaction in a random magnetic field using exact diagonalization. In order to obtain many-body mobility edge at infinite temperature, we employ a polynomial filtered Lanczos method that can avoid the fill-in problem when implementing the commonly used shift-and-invert transformation. In stark contrast to the original Heisenberg model, although the localized phase always conforms to Poisson statistics, the ergodic phase exhibits the Gaussian unitary ensemble rather than the Gaussian orthogonal ensemble statistics due to the lack of complex conjugation symmetry. The boundary between the ergodic and localized phases is determined by carefully performing finite-size scalings for the level statistics, entanglement entropy and its standard deviation, as well as fluctuations of the total spin of the system. The two phases are also well distinguished by the full delocalization or localization in the Hilbert space wherein the participation entropies present. To indicate the localized phase in experiment, we propose a scheme for realizing the out-of-time-order correlator on a modern nuclear magnetic resonance quantum simulator.