## SciPost Submission Page

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

### by Patrick Emonts, Erez Zohar

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

### Submission summary

As Contributors: | Patrick Emonts |

Arxiv Link: | https://arxiv.org/abs/1807.01294v4 |

Date accepted: | 2020-01-07 |

Date submitted: | 2019-12-20 |

Submitted by: | Emonts, Patrick |

Submitted to: | SciPost Physics Lecture Notes |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approaches: | Theoretical, Computational |

### 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.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. Lect. Notes 12 (2020)

### Author comments upon resubmission

### List of changes

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