Illinois Mobile App Master Calendar

Speaker: Eric Roon
Title: Ergodic Matrix Product States 

Abstract: Movassagh—Schenker (2021) proved a multiplicative ergodic theorem for so-called ergodic quantum processes of random unital completely positive maps. One of the principal applications of their result was to show that ergodic matrix product states converge almost surely in the thermodynamic limit. In this talk, we will discuss recent work by R. — Schenker (2025) which proves an MPS-type factorization for disordered finitely correlated states in terms of ergodic quantum processes when the underlying disorder space is a topological dynamical system. We discuss a disordered version of the AKLT model for which a.) the spectral gap closes almost surely, and b.) is invariant under time reversal symmetry, and has a nontrivial Tasaki index in spite of the disorder. If time permits, we will discuss some current and future directions in ergodic matrix product states in progress with Ekblad, Moreno-Nadales, R., and Schenker.

This is the weekly seminar of the Quantum Working Group in the Department of Mathematics. For questions, please reach out to Marius Junge, Gabriele La Nave, Felix Leditzky, or Amanda Young.