Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model

TL;DR

This paper uncovers exotic quantum phases in a constrained Bose-Hubbard model, including a dipole Luttinger liquid and a dipole supersolid, using theoretical mapping and tensor network simulations.

Contribution

It demonstrates the existence of fracton-related phases in a 1D Bose-Hubbard model through novel mappings and combined analytical and numerical methods.

Findings

Identification of a dipole Luttinger liquid phase.

Discovery of a robust dipole supersolid state.

Numerical evidence supporting coexistence of orderings.

Abstract

Quantum many-body systems with fracton constraints are widely conjectured to exhibit unconventional low-energy phases of matter. In this work, we demonstrate the existence of a variety of such exotic quantum phases in the ground states of a dipole-moment conserving Bose-Hubbard model in one dimension. For integer boson fillings, we perform a mapping of the system to a model of microscopic local dipoles, which are composites of fractons. We apply a combination of low-energy field theory and large-scale tensor network simulations to demonstrate the emergence of a dipole Luttinger liquid phase. At non-integer fillings our numerical approach shows an intriguing compressible state described by a quantum Lifshitz model in which charge density-wave order coexists with dipole long-range order and superfluidity - a `dipole supersolid'. While this supersolid state may eventually be unstable against lattice effects in the thermodynamic limit, its numerical robustness is remarkable. We discuss potential experimental implications of our results.