2020/06/30 by Maxime Dupont, Nicolas Laflorencie, Gabriel Lemarié
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Boson #Cold Atom Physics and Bose-Einstein Condensates #Ergodicity #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Position and momentum space #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Randomness #Statistical physics #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.174205
published as Phys. Rev. B 102, 174205 (2020) · 21 pages, 16 figures
arxiv created 2020/11/19 · openalex publication_date 2020/11/19 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.