Entanglement renormalization and gauge symmetry

          @misc{ pirsa_PIRSA:10050066,
            doi = {10.48660/10050066},
            url = {https://pirsa.org/10050066},
            author = {Vidal, Guifre},
            keywords = {Quantum Information},
            language = {en},
            title = {Entanglement renormalization and gauge symmetry},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050066 see, \url{https://pirsa.org}}
          }
          

Abstract

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints, and it can be regarded as the low energy limit of a lattice model with a local symmetry. I will describe a coarse-graining scheme capable of exactly preserving local symmetries. The approach results in a variational ansatz for the ground state(s) and low energy excitations of a lattice gauge theory. This ansatz has built-in local symmetries, which are exploited to significantly reduce simulation costs. I will describe benchmark results in the context of Kitaev’s toric code with a magnetic field or, equivalently, Z2 lattice gauge theory, for lattices with up to 16 x 16 sites (16^2 x 2 = 512 spins) on a torus.