QLunch: Martin Dam Larsen

Speaker: Martin Dam Larsen

Title: Sharp Widom Conjecture and Area Laws for Translation-Invariant Quasi-Free Fermions. 

Abstract: Gioev and I. Klich observed that the entanglement entropy of translation-invariant free fermions is governed by a conjecture made by Widom on Szegö asymptotics for pseudodifferential operators with discontinuities in both position and momentum. In this talk, we will explain the precise mechanism behind this connection and how entanglement entropy reduces to a singular Szegö-type problem. We then formulate and prove sharp versions of the Widom conjecture with minimal smoothness assumptions. Finally, we discuss the the transition from smooth to singular symbols, corresponding physically to a gap closing or the zero-temperature limit.

Joint work with Søren Fournais, Robert Seiringer, Jan Philip Solovej.