Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

摘要: Author(s): Dupont, M; Laflorencie, N; Lemarie, G | Abstract: © 2020 American Physical Society. Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential site-centered Cayley trees with branching number K=2. In order to follow how Bose-Einstein condensate (BEC) is affected by disorder, focus both zero-momentum density, probing coherence, and one-body density matrix (1BDM) whose largest eigenvalue monitors off-diagonal long-range order. We further study its associated eigenstate which brings useful information about real-space properties this leading eigenmode. Upon increasing randomness, find that system undergoes transition at finite disorder strength between ordered BEC state, fully ergodic large scale, new disordered Bose glass regime showing conventional localization for coherence fraction while 1BDM displays nontrivial algebraic vanishing together nonergodic occupation real space. These peculiar can be analytically captured simple phenomenological description tree provides physical picture regime.