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

Understand

We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states.

• We do so by introducing a family of one-dimensional local quantum rotor and 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.
• 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.