Particle Physics Seminar: Gauging PEPS: Constructing and Studying Tensor Networks with Local Gauge Invariance

Abstract:

In the recent years, tensor network constructions have proven very useful for the study of quantum many body models, in particular in the context of condensed matter physics. Tensor network constructions such as PEPS (Projected Entangled Pair States) and its one dimensional version, MPS (Matrix Product State) offer, besides their built-in entanglement entropy area law, a very natural, fundamental approach for encoding and classifying symmetries. As such, they have been used extensively for the study of globally symmetric many body models - including variational, numerical studies, mostly using MPS in 1d, but also with other approaches in higher dimensions, offering some analytical insights on many body theories.

In my talk, I will focus on more recent PEPS developments, that have to do with their generalization to describe local symmetries as well, allowing to extend the set of models studied with tensor networks to gauge theories, as in the standard model of particle physics, or various condensed matter contexts. As fundamental as they are, gauge theories still face several difficult challenges, and therefore new tools are always very important for their study.

I will review the basics of PEPS with global symmetries, and then focus on the local extensions to lattice gauge theory states, give some examples for explicit constructions of PEPS involving fermionic matter and gauge fields, and finally comment on a recent classification of gauge invariant MPS (PEPS in 1d).

Seminar Organizer: Prof. Nissan Itzhaki