Topological invariants for SPT entanglers

TL;DR

This paper introduces a framework to classify and compute topological invariants of locality-preserving unitaries that generate symmetry-protected topological phases, with applications to Floquet phases and entanglers.

Contribution

It develops a novel classification framework for LPUs with symmetries using flux insertion operators, providing explicit formulas for topological invariants of SPT entanglers.

Findings

Formulas for topological invariants of LPUs in various dimensions.

Edge invariants for Floquet topological phases.

Closed-form expressions for 1D and some higher-dimensional SPT entanglers.

Abstract

We develop a framework for classifying locality preserving unitaries (LPUs) with internal, unitary symmetries in $d$ dimensions, based on $(d-1)$ dimensional ``flux insertion operators" which are easily computed from the unitary. Using this framework, we obtain formulas for topological invariants of LPUs that prepare, or entangle, symmetry protected topological phases (SPTs). These formulas serve as edge invariants for Floquet topological phases in $(d+1)$ dimensions that ``pump" $d$-dimensional SPTs. For 1D SPT entanglers and certain higher dimensional SPT entanglers, our formulas are completely closed-form.