Signatures of many-body localisation in the dynamics of two-sites entanglement

TL;DR

This paper demonstrates that two-site entanglement dynamics, measured via concurrence, reveals clear signatures of many-body localisation, distinguishing it from Anderson localisation and ergodic phases through power-law and exponential decay behaviors.

Contribution

It introduces a method to detect many-body localisation signatures using two-site entanglement dynamics, supported by numerical and analytical results, and suggests experimental feasibility.

Findings

Power-law decay of entanglement in MBL phase

Plateau in entanglement for Anderson localisation

Exponential decay in ergodic phase

Abstract

We are able to detect clear signatures of dephasing -- a distinct trait of Many-Body Localisation (MBL) -- via the dynamics of two-sites entanglement, quantified through the concurrence. Using the protocol implemented in [Science {\bf 349}, 842 (2015)] we show that -- in the MBL phase -- the average two-site entanglement decays in time as a power law, while in the Anderson localised phase it tends to a plateau. The exponent of the power law is not universal and shows a clear dependence on the strength of the interaction. This behaviour is also qualitatively different in the ergodic phase where the two-site entanglement decays exponentially. All the results are obtained by means of time-dependent density matrix renormalisation group simulations; they are corroborated by analytical calculations on an effective model. Two-site entanglement has been already measured in cold atoms: Our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase.