Entanglement renormalization and gauge symmetry

Abstract

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints, and can be regarded as the low energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low energy, effective descriptions of lattice models with a local symmetry, such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure, and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of the toric code with a magnetic field, equivalent to Z2 lattice gauge theory, for lattices with up to 16 x 16 sites (16^2 x 2 = 512 spins) on a torus. We reproduce the well-known ground state phase diagram of the model, consisting of a deconfined and spin polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground state fidelities, Wilson loops, and several other quantities.

reviewed version as published in PRB; this version includes a new section about the accuracy of the results several corrections and added citations

References in corpus (20)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Ground state fidelity from tensor network representations
• Entanglement renormalization and topological order
• Quantum fidelity and quantum phase transitions in matrix product states
• Entanglement renormalization, scale invariance, and quantum criticality
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Adiabatic Preparation of Topological Order
• Quantum MERA Channels
• Exact entanglement renormalization for string-net models
• Symmetry breaking and criticality in tensor-product states
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States
• Direct numerical computation of disorder parameters