SciPost Physics Lecture Notes

SciPost Phys. Lect. Notes 12 (2020) · published 17 January 2020

• doi: 10.21468/SciPostPhysLectNotes.12
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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.

• Ashkenazi et al., Duality as a feasible physical transformation for quantum simulation
  Phys. Rev. A 105, 022431 (2022) [Crossref]
• Zohar, Local manipulation and measurement of nonlocal many-body operators in lattice gauge theory quantum simulators
  Phys. Rev. D 101, 034518 (2020) [Crossref]
• Zhang et al., Selected topics of quantum computing for nuclear physics*
  Chinese Phys. B 30, 020306 (2021) [Crossref]
• Franco-Rubio et al., Entanglement renormalization for gauge invariant quantum fields
  Phys. Rev. D 103, 025013 (2021) [Crossref]
• Roose et al., Lattice regularisation and entanglement structure of the Gross-Neveu model
  J. High Energ. Phys. 2021, 207 (2021) [Crossref]
• Riechert et al., Engineering a U(1) lattice gauge theory in classical electric circuits
  Phys. Rev. B 105, 205141 (2022) [Crossref]
• Kelman et al., Gauged Gaussian projected entangled pair states: A high dimensional tensor network formulation for lattice gauge theories
  Phys. Rev. D 110, 054511 (2024) [Crossref]
• Emonts et al., Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1D Z2 demonstration
  Phys. Rev. D 107, 014505 (2023) [Crossref]
• Mortier et al., Finite-Entanglement Scaling of 2D Metals
  Phys. Rev. Lett. 131, 266202 (2023) [Crossref]
• Akiyama et al., Tensor renormalization group for fermions
  J. Phys.: Condens. Matter 36, 343002 (2024) [Crossref]
• Gustafson et al., Toward quantum simulations ofZ2gauge theory without state preparation
  Phys. Rev. D 103, 054507 (2021) [Crossref]
• Zohar, Wilson loops and area laws in lattice gauge theory tensor networks
  Phys. Rev. Research 3, 033179 (2021) [Crossref]
• Emonts et al., Variational Monte Carlo simulation with tensor networks of a pureZ3gauge theory in(2+1)D
  Phys. Rev. D 102, 074501 (2020) [Crossref]