Fractonic superfluids. III. Hybridizing higher moments

Abstract

Fractonic superfluids are featured by the interplay of spontaneously broken charge symmetry and mobility constraints on single-particle kinematics due to the conservation of higher moments, such as dipoles, angular charge moments, and quadrupoles. Building on prior studies by Yuan \textit{et al.} [\href{https://doi.org/10.1103/PhysRevResearch.2.023267}{Phys. Rev. Res. 2, 023267 (2020)}] and Chen \textit{et al.} [\href{https://doi.org/10.1103/PhysRevResearch.3.013226}{Phys. Rev. Res. 3, 013226 (2021)}], we study a class of fractonic superfluids, termed \textit{hybrid fractonic superfluids} (HFS), in which bosons of multiple species interact while moment hybridization is conserved. We explore the consequences of hybridization via two model series: \textit{Model Series A}, conserving total moments of the same order across species, and \textit{Model Series B}, conserving total moments of different orders. In Model Series A, we analyze dipole moment hybridization and extend the discussion to higher-order moments, examining the ground state, Goldstone modes, correlation functions, and so on. We compute the minimal spatial dimensions, where the total charge symmetry begins to get partially broken via particle-hole condensation, leading to true off-diagonal long-range order. In Model Series B, we focus on HFS with hybrid dipole-quadrupole conservation. For both series, we introduce Bose-Hubbard-type lattice models that reduce to either of both series in the weak Hubbard interaction regime. We perform a mean-field analysis on the global phase diagram and discuss experimental realizations in strongly tilted optical lattices via a third-order perturbation theory. This work, alongside prior studies, completes a trilogy on fractonic superfluids, uncovering symmetry-breaking physics emerging from higher moment conservation, leaving various promising studies for future investigation.