Filling constraints on translation invariant dipole conserving systems

TL;DR

This paper investigates the conditions under which one-dimensional translation-invariant systems with dipole and charge conservation have a unique, gapped ground state, revealing that both charge and dipole fillings, along with boundary conditions, are crucial.

Contribution

It establishes the combined role of charge and dipole fillings, and boundary conditions, in determining the ground state properties of dipole-conserving systems, contrasting previous assumptions.

Findings

A symmetric, gapped, non-degenerate ground state requires integer charge and fixed dipole filling.

Fractional dipole fillings lead to gapless or symmetry-breaking ground states.

Dipole filling constraints depend on system size and boundary conditions.

Abstract

Systems with conserved dipole moment have drawn considerable interest in light of their realization in recent experiments on tilted optical lattices. An important question for such systems is delineating the conditions under which they admit a unique gapped ground state that is consistent with all symmetries. Here, we study one-dimensional translation-invariant lattices that conserve U(1) charge and $\mathbb{Z}_L$ dipole moment, where discreteness of the dipole symmetry is enforced by periodic boundary conditions, with $L$ the system size. We show that in these systems, a symmetric, gapped, and non-degenerate ground state requires not only integer charge filling, but also a fixed value of the dipole filling, while other fractional dipole fillings enforce either a gapless or symmetry-breaking ground state. In contrast with prior results in the literature, we find that the dipole filling constraint depends both on the charge filling as well as the system size, emphasizing the subtle interplay of dipole symmetry with boundary conditions. We support our results with numerical simulations and exact results.