Can we study the many-body localisation transition?
arXiv:1911.07882 · doi:10.1209/0295-5075/128/67003
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.
Close to published version. 8+2 pages, 4+2 figures
References in corpus (12)
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Many-body localization edge in the random-field Heisenberg chain
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- Integrals of motion in the Many-Body localized phase
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Recent progress in many-body localization
- Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
- Ergodicity breaking in a model showing many-body localization
- Anomalous thermalization in ergodic systems
- Many-body localization dynamics from gauge invariance