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

TL;DR

This paper explores how spatially modulated conserved quantities in generalized Bose-Hubbard models lead to exotic quantum liquids, Hilbert space fragmentation, and phase transitions characterized by Luttinger liquids and vortex unbinding.

Contribution

It introduces models conserving finite Fourier momenta of particle number, revealing novel Hilbert space fragmentation and analyzing phase diagrams with analytical and numerical methods.

Findings

Hilbert space fragmentation for incommensurate momenta

Phase transition between Mott insulator and Luttinger liquid

Possible Berezinskii-Kosterlitz-Thouless transition driven by vortex unbinding

Abstract

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. This is linked to the nature of the conserved quantities having a dense spectrum and provides the first such example. We then characterize the zero-temperature 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, we derive a dual description, from where we estimate the robustness of this phase using renormalization group arguments, where the driving perturbation has ultra-local correlations in space but power law correlations in time. We support this conclusion using an equivalent representation of the system as a two-dimensional vortex gas with modulated Coulomb interactions within a fixed symmetry sector. We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.