Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
Abstract
Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number K =2 . In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a nontrivial algebraic vanishing BEC density together with a nonergodic occupation in real space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime.
- Publication:
-
Physical Review B
- Pub Date:
- November 2020
- DOI:
- 10.1103/PhysRevB.102.174205
- arXiv:
- arXiv:2006.15465
- Bibcode:
- 2020PhRvB.102q4205D
- Keywords:
-
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 21 pages, 16 figures