## Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

Patrick Emonts, Erez Zohar

SciPost Phys. Lect. Notes 12 (2020) · published 17 January 2020

- doi: 10.21468/SciPostPhysLectNotes.12
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### Abstract

In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

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^{1}Patrick Emonts, -
^{2}Erez Zohar

^{1}Max-Planck-Institut für Quantenoptik / Max Planck Institute of Quantum Optics [MPQ]^{2}האוניברסיטה העברית בירושלים / Hebrew University of Jerusalem [HUJI]