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Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories

by Patrick Emonts, Erez Zohar

This Submission thread is now published as SciPost Phys. Lect. Notes 12 (2020)

Submission summary

As Contributors: Patrick Emonts
Arxiv Link: (pdf)
Date accepted: 2020-01-07
Date submitted: 2019-12-20 01:00
Submitted by: Emonts, Patrick
Submitted to: SciPost Physics Lecture Notes
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


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.

Ontology / Topics

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Gauge theory Lattice fermions Projected Entangled Paired States (PEPS) Tensor networks

Published as SciPost Phys. Lect. Notes 12 (2020)

Author comments upon resubmission

We would like to thank Luca Tagliacozzo for the second review and for taking the time to prepare the accompanying note. Indeed we agree with him on the physics, and the only disagreement was lexical. Therefore, we modified the manuscript accordingly.

List of changes

We modified the last paragraph of 4.3 to contain the extra information requested by the referee.

Submission & Refereeing History

Published as SciPost Phys. Lect. Notes 12 (2020)

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Resubmission 1807.01294v4 on 20 December 2019

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