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

TL;DR

This study uses quantum Monte Carlo simulations to explore how disorder affects Bose-Einstein condensation and ergodicity in hard-core bosons on Cayley trees, revealing a transition to a Bose glass phase with unique localization and non-ergodic properties.

Contribution

It provides the first detailed analysis of the interplay between disorder, BEC, and ergodicity breaking on Cayley trees, introducing a phenomenological model for the Bose glass phase.

Findings

Quantum phase transition at finite disorder strength

Emergence of a Bose glass regime with non-trivial properties

Localization of coherence and non-ergodic occupation in the Bose glass

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 non-trivial algebraic vanishing BEC density together with a non-ergodic 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.