Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries

TL;DR

This paper demonstrates that twisted boundary conditions reveal ground state degeneracies in quantum many-body systems with discrete symmetries, providing evidence for Lieb-Schultz-Mattis type ingappability in higher dimensions.

Contribution

It establishes a connection between twisted boundary conditions and ground state degeneracy, extending Lieb-Schultz-Mattis theorems to systems with discrete symmetries in higher dimensions.

Findings

Ground state degeneracy under twisted boundary conditions for systems with projective symmetry representations.

Gapped systems exhibit ground state degeneracy under periodic boundary conditions due to twisted boundary conditions.

Supports the Lieb-Schultz-Mattis ingappability conjecture in two and higher dimensions.

Abstract

We discuss quantum many-body systems with lattice translation and discrete onsite symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell forms a projective representation of the onsite discrete symmetry. Based on the quantum transfer matrix formalism, we show that, if the system is gapped, the ground-state degeneracy under the twisted boundary condition also implies a ground-state (quasi-)degeneracy under the periodic boundary conditions. This gives a compelling evidence for the recently proposed Lieb-Schultz-Mattis type ingappability due to the onsite discrete symmetry in two and higher dimensions.