Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries

After an extended introduction to recent developments on the role of unconventional symmetries in quantum many-body systems, we investigate the effect that spatially modulated conserved quantities can have on quantum ground states. We do so by introducing a family of one-dimensional bosonic models which conserve finite Fourier momenta of the particle number, but not the particle number itself. These correspond to generalizations of the standard Bose-Hubbard model (BHM), and relate to the physics of Bose surfaces and the dipolar BHM.

First, we show that while having an infinite-dimensional local Hilbert space, such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice. This is linked to the nature of the conserved quantities having a dense spectrum and provides the first such example. We then characterize the ground state phase diagram for both commensurate and incommensurate momenta. In both cases, analytical and numerical calculations predict a phase transition between a gapped (Mott insulating) and quasi-long range order phase; the latter is characterized by a two-species Luttinger liquid in the infrared, but dressed by oscillatory contributions when computing microscopic expectation values. Following a rigorous Villain formulation of the corresponding rotor model in terms of height field variables, we compute two-point correlation functions, ultra-local for incommensurate momenta, and estimate the robustness of this phase using renormalization group arguments. This is further supported by an equivalent interpretation of the phase as a two-dimensional vortex gas even within a fixed symmetry sector.

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