Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators

TL;DR

This paper investigates the symmetry-resolved entanglement in $C_2$-symmetric topological insulators, establishing bounds on entropy based on a topological invariant derived from symmetry considerations.

Contribution

It introduces a new topological invariant for fermionic ground states in $C_2$-symmetric systems and links it to entropy bounds, providing a novel theoretical framework.

Findings

The invariant $ ext{Delta}$ is an adiabatic invariant for the system.

Entropy bounds can be directly computed from high symmetry points.

The results apply to band insulators with $C_2$ symmetry.

Abstract

For a many-body system of arbitrary dimension, we consider fermionic ground states of non-interacting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $\Delta$ between the number of occupied symmetric and anti-symmetric single-particle states is an adiabatic invariant. We prove lower bounds on the configurational and the number entropy based on this invariant. In band insulators, the topological invariant $\Delta$ and the entropy bounds can be directly determined from high symmetry points in the Brillouin zone.