Erez Zohar
Published 2018-07-03Version 1
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.
Comments: Notes prepared for two lectures given in the Focus week "Tensor Networks and Entanglement" of the workshop "Entanglement in Quantum System", at the Galileo Galilei Institute for Theoretical Physics (GGI), Florence, Italy in June 2018
Quantum Simulation of Quantum $\mathbb{Z}_2$ Gauge Theory demonstrated in a GPU Simulator
Duality transformations and the entanglement entropy of gauge theories
Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories
![QR code for arXiv:1807.01294 [quant-ph]](http://oss.arxitics.com/images/favicon.svg)