Genuine multipartite entanglement as a probe of many-body localization in disordered spin chains with Dzyaloshinskii-Moriya interactions

TL;DR

This paper shows that genuine multipartite entanglement effectively distinguishes between ergodic and many-body localized phases in disordered spin chains, with Dzyaloshinskii-Moriya interactions influencing the transition point.

Contribution

It introduces GME as a reliable indicator for the ergodic-MBL transition in disordered spin models with Dzyaloshinskii-Moriya interactions, highlighting the impact of these interactions on localization.

Findings

GME approaches maximum in the ergodic phase.

GME vanishes in the MBL phase, both statically and dynamically.

DM interactions delay the localization transition.

Abstract

We demonstrate that the quenched average genuine multipartite entanglement (GME) can approach its maximum value in the ergodic phase of a disordered quantum spin model. In contrast, GME vanishes in the many-body localized (MBL) phase, both in equilibrium and in the long-time dynamical steady state, indicating a lack of useful entanglement in the localized regime. To establish this, we analyze the disordered Heisenberg spin chain subjected to a random magnetic field and incorporating two- and three-body Dzyaloshinskii-Moriya (DM) interactions. We exhibit that the behavior of GME, in both static eigenstates and in dynamically evolved states from an initial Neel configuration, serves as a reliable indicator of the critical disorder strength required for the ergodic-to-MBL transition. The identified transition point aligns well with standard indicators such as the gap ratio and correlation length. Moreover, we find that the presence of DM interactions, particularly the three-body one, significantly stabilizes the thermal phase and delays the onset of localization. This shift in the transition point is consistently reflected in both static and dynamical analyses, reinforcing GME as a robust probe for MBL transitions.