Phase Space Entanglement Spectrum

TL;DR

This paper introduces a new class of entanglement cuts in phase space for free fermionic systems, revealing topological features and symmetries that interpolate between position and momentum space.

Contribution

It generalizes entanglement spectra to phase space cuts and uncovers topological properties and symmetries in these spectra for inversion symmetric wavefunctions.

Findings

Phase space entanglement spectra can be explicitly computed for free fermions.

The spectra exhibit chiral symmetry for inversion symmetric states.

A topological index can be associated with the phase space entanglement spectrum.

Abstract

We generalize the position- and momentum-space entanglement cuts to a family of cuts corresponding to regions in the classical phase space. We explicitly compute the entanglement spectra of free fermionic many-body wavefunctions for a family of phase space entanglement cuts that continuously interpolates between position- and momentum-space cuts. For inversion symmetric wavefunctions, the phase space entanglement spectrum possess a chiral symmetry, to which a topological index can be associated.