Many-Body Fu–Kane–Mele Index

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.