Entanglement of free-fermion systems, signal processing and algebraic combinatorics

Abstract

This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band limiting problems is used to obtain a tridiagonal matrix commuting with the chopped correlation matrix in bispectral situations and on the other, the irreducible decomposition of the Terwilliger algebra arising in the context of $P$-polynomial association schemes is seen to yield a simplifying framework.

11 pages; This paper is based on the presentation made by Luc Vinet at Gravity, Strings and Fields: A conference in honour of Gordon Semenoff organized by the CRM. v2: Minor modifications to match the published version