Many-body Fu-Kane-Mele index

TL;DR

This paper introduces a new $$-valued index for 2D interacting fermionic systems with charge conservation and time reversal symmetry, extending the Fu-Kane-Mele index to include interactions.

Contribution

It defines a topological index for interacting systems that generalizes the Fu-Kane-Mele index from free to interacting fermionic topological insulators.

Findings

The index is non-trivial when the fluxon transforms as a Kramers pair.

The index characterizes the topological phase of interacting fermionic systems.

It provides a tool to distinguish topological phases beyond free fermion models.

Abstract

We define a $\mathbb{Z}_2$-valued index for stably short-range entangled states of two-dimensional fermionic lattice systems with charge conservation and time reversal symmetry. The index takes its non-trivial value precisely if the `fluxon', the state obtained by inserting a $\pi$-flux through the system, transforms under time reversal as part of a Kramers pair. This index extends the Fu-Kane-Mele index of free fermionic topological insulators to interacting systems.