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.
Cited by 3
Erez Zohar, Local manipulation and measurement of nonlocal many-body operators in lattice gauge theory quantum simulators
Phys. Rev. D 101, 034518 (2020) [Crossref]
Adrián Franco-Rubio et al., Entanglement renormalization for gauge invariant quantum fields
Phys. Rev. D 103, 025013 (2021) [Crossref]
Patrick Emonts et al., Variational Monte Carlo simulation with tensor networks of a pure
gauge theory in
Phys. Rev. D 102, 074501 (2020) [Crossref]
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- 1 Max-Planck-Institut für Quantenoptik / Max Planck Institute of Quantum Optics [MPQ]
- 2 האוניברסיטה העברית בירושלים / Hebrew University of Jerusalem [HUJI]