Calendar of Events

Speaker: Ilya Vilkoviskiy - Princeton University

Abstract:  

The influence matrix (IM) provides an efficient framework for simulating quantum dynamics and has been successfully applied to impurity models as well as to strongly interacting chaotic systems. In the case of impurity models, the IM enables polynomial-time algorithms for simulating dynamical correlation functions, together with rigorous complexity bounds. Motivated by this success, I will explore extensions of the IM approach to integrable systems.

I will introduce XXZ-type integrable temporal transfer matrices, for which the IM can be interpreted as a Bethe vector. These matrices define a novel integrable structure due to their non-diagonalizability, featuring thermodynamically large Jordan blocks. The structure of these blocks will be analyzed explicitly in the noninteracting XX spin chain, yielding the distribution of their sizes and the structure of the corresponding wave functions.

Host: Natan Andrei