Bose-Einstein condensation in quantum glasses

The role of geometrical frustration in strongly interacting bosonic systems is studied with a combined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behaviour. The differences between such a phase and the otherwise insulating “Bose glasses” are elucidated.

💡 Research Summary

The paper investigates how geometric frustration influences strongly interacting bosonic systems at ultra‑low temperatures, focusing on the emergence of a quantum phase that simultaneously exhibits Bose‑Einstein condensation (BEC) and spin‑glass behavior. The authors study the Bose‑Hubbard model placed on a random regular graph (RRG), a network where each site has a fixed coordination number but the connections are randomly assigned. This topology introduces short loops and a high degree of frustration, mimicking the disorder found in glassy materials while preserving a mean‑field‑like environment suitable for analytical treatment.

Two complementary approaches are employed. First, large‑scale quantum Monte‑Carlo (QMC) simulations using the Stochastic Series Expansion algorithm are performed on systems up to 10⁴ sites, reaching inverse temperatures βt ≥ 30 to approach the ground‑state regime. The simulations directly measure the condensate fraction ρ₀ = ⟨b⟩², the superfluid stiffness D, and the Edwards‑Anderson order parameter q_EA =