Lieb-Schultz-Mattis type constraints on Fractonic Matter

TL;DR

This paper extends Lieb-Schultz-Mattis constraints to fractonic systems with subsystem symmetries, revealing conditions for gapped ground states and ground state degeneracy, and connecting these to boundary anomalies in SSPT states.

Contribution

It formulates LSM-type constraints for fracton phases with subsystem symmetries, providing new conditions for ground state properties and their topological implications.

Findings

Integer filling and polarization are required for symmetric, gapped, non-degenerate ground states.

Constraints on ground state degeneracy when conditions are not met.

Mapping between subsystem symmetry constraints and boundary anomalies in SSPT states.

Abstract

The Lieb-Schultz-Mattis (LSM) theorem and its descendants impose strong constraints on the low-energy behavior of interacting quantum systems. In this paper, we formulate LSM-type constraints for lattice translation invariant systems with generalized U(1) symmetries which have recently appeared in the context of fracton phases: U(1) polynomial shift and subsystem symmetries. Starting with a generic interacting system with conserved dipole moment, we examine the conditions under which it supports a symmetric, gapped, and non-degenerate ground state, which we find requires that both the filling fraction and the bulk charge polarization take integer-values. Similar constraints are derived for systems with higher moment conservation laws or subsystem symmetries, in addition to lower bounds on the ground state degeneracy when certain conditions are violated. Finally, we discuss the mapping between LSM-type constraints for subsystem symmetries and the anomalous symmetry action at boundaries of subsystem symmetric topological (SSPT) states.