Finite-size scaling of many-body localization phase transitions
Abstract
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside the framework of statistical mechanics as they involve the breakdown of ergodicity. Here, we consider what general constraints can be imposed on the nature of eigenstate transitions due to the presence of disorder. We derive Harris-type bounds on the finite-size scaling exponents of the mean entanglement entropy and level statistics at the many-body localization phase transition using several different arguments. Our results are at odds with recent small-size numerics, for which we estimate the crossover scales beyond which the Harris bound must hold.
- Publication:
-
Aspects and Applications of Many-Body Localization
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1509.04285
- arXiv:
- arXiv:1509.04285
- Bibcode:
- 2015aamb.confE...3C
- Keywords:
-
- Condensed matter;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 6 pages