Can we study the many-body localisation transition?

¹ The Abdus Salam International Centre for Theoretical Physics - Strada Costiera 11, 34151 Trieste, Italy
² SISSA - Via Bonomea 265, 34136 Trieste, Italy
³ INFN, Sezione di Trieste - Via Valerio 2, 34126 Trieste, Italy
⁴ Physics Department, Faculty of Mathematics and Physics, University of Ljubljana - Jadranska 19, SI-1000 Ljubljana, Slovenia

^(a) staylor@ictp.it (corresponding author)

Received: 29 November 2019
Accepted: 7 January 2020

Abstract

We present a detailed analysis of the length- and timescales needed to approach the critical region of MBL from the delocalised phase, studying both eigenstates and the time evolution of an initial state. For the eigenstates we show that in the delocalised region there is a single length, which is a function of disorder strength, controlling the finite-size flow. Small systems look localised, and only for larger systems do resonances develop which restore ergodicity in the form of the eigenstate thermalisation hypothesis. For the transport properties, we study the time necessary to transport a single spin across a domain wall, showing how this grows quickly with increasing disorder, and compare it with the Heisenberg time. For a sufficiently large system the Heisenberg time is always larger than the transport time, but for a smaller system this is not necessarily the case. We conclude that the properties of the MBL transition cannot be explored using the system sizes or times available to current numerical and experimental studies.