Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks

Abstract

Tensor network states have been a very prominent tool for the study of quantum many-body physics, thanks to their physically relevant entanglement properties and their ability to encode symmetries. In the last few years, the formalism has been extended and applied to theories with local symmetries to - lattice gauge theories. In the contraction of tensor network states as well as correlation functions of physical observables with respect to them, one uses the so-called transfer operator, whose local properties dictate the long-range behaviour of the state. In this work we study transfer operators of tensor network states (in particular, PEPS - projected entangled pair states) in the context of lattice gauge theories, and consider the implications of the local symmetry on their structure and properties. We focus on the Wilson loop - a nonlocal, gauge-invariant observable which is central to pure gauge theories, whose long range decay behaviour probes the confinement or deconfinement of static charges. Using the symmetry, we show how to handle its contraction, and formulate conditions relating local properties to its decay fashion.

References in corpus (20)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Criticality, the area law, and the computational power of PEPS
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Entanglement renormalization and gauge symmetry
• Lattice Gauge Tensor Networks
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Chiral projected entangled-pair state with topological order
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States
• Wegner-Wilson loops in string nets

Cited by in corpus (5)

• Entanglement generation in $(1+1)D$ QED scattering processes
• Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Entanglement and confinement in lattice gauge theory tensor networks
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach