TensorTalk: Quantum Wielandt Theorems

Speaker: Vladimir Lysikov

Title: Quantum Wielandt Theorems

Abstract: We discuss quantum Wielandt theorems which show that a large enough part of an MPS or PEPS network can give any tensor on the outgoing edges.

This is used show that any PEPS is a ground state of some local Hamiltonian (parent Hamiltonian) and give bounds on the interaction length of the parent Hamiltonian for MPS.

The talk is based on papers by Michałek and Shitov (https://arxiv.org/pdf/1809.04387.pdf) and Michałek, Seyennaeve, Verstraete (https://arxiv.org/pdf/1811.05502.pdf).