Quantum many-body effects in a pi-flux Hubbard model

Frustration and synthetic magnetic fluxes have emerged as pivotal tools in the exploration of novel many-body quantum phases in ultracold atomic systems. A particularly non-trivial framework involves the introduction of a pi-flux, which gives rise to topologically non-trivial band structures and enables spontaneous breaking of time-reversal symmetry, a key feature in the emergence of chiral phases. Building on recent two-dimensional studies, we investigate the many-body physics of a three-dimensional generalization of the pi-flux Bose-Hubbard model, involving bosonic particles on strongly dimerized cubic plaquettes. We construct a low-energy effective model that we benchmark via exact diagonalization of the full model, revealing filling-dependent degeneracies and regularities in the energy spectrum. These regularities hint at the presence of underlying hidden symmetries in the model, that we attempt to classify by developing a group theory analysis and recasting the effective Hamiltonian in terms of an SU(4) algebraic description. In the weakly interacting regime, a Gross–Pitaevskii analysis uncovers a 12-fold degenerate manifold of classical ground states characterized by chiral loop current patterns flowing on the edges of the cubic cell. Our results establish the 3D pi-flux cube as a minimal model for investigating many-body physics in higher dimensions and novel chiral states relevant for quantum simulation platforms based on ultra-cold atoms in synthetic gauge fields.