Back to Videos
This is a video about Classical restrictions of MPS are Gibbsian

Classical restrictions of MPS are Gibbsian

February 8, 2021
IPAM
Presenters: Michael Kastoryano
Length: 20 minutes 39 seconds

Watch Video 

Abstract

Michael Kastoryano - Amazon

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local Hamiltonians (i.e., are quasi-locally Gibbsian) if the classical conditional mutual information (CMI) of any connected tripartition of the lattice is rapidly decaying in the width of the middle region. For injective matrix product states, we moreover show that the classical CMI decays exponentially, whenever the collection of matrix product operators satisfies a ‘purity condition’; a notion previously established in the theory of random matrix products.

Download Abstract