## SciPost Submission Page

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

### by Patrick Emonts, Erez Zohar

### Submission summary

As Contributors: | Patrick Emonts |

Arxiv Link: | https://arxiv.org/abs/1807.01294v2 |

Date submitted: | 2019-08-08 |

Submitted by: | Emonts, Patrick |

Submitted to: | SciPost Physics Lecture Notes |

Domain(s): | Theor. & Comp. |

Subject area: | Quantum Physics |

### 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.