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 (44)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The phase diagram of dense QCD
• FLAG Review 2019
• Criticality, the area law, and the computational power of PEPS
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• The mass spectrum of the Schwinger model with Matrix Product States
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• QCD as a Quantum Link Model
• Review on novel methods for lattice gauge theories
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Matrix product states for gauge field theories
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Non-Abelian string breaking phenomena with Matrix Product States
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Entanglement renormalization and gauge symmetry
• 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 Gauge Tensor Networks
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Real-time simulation of the Schwinger effect with Matrix Product States
• Chiral condensate in the Schwinger model with Matrix Product Operators
• Hamiltonian simulation of the Schwinger model at finite temperature
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Chiral projected entangled-pair state with topological order
• Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
• Building Projected Entangled Pair States with a Local Gauge Symmetry
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
• 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
• Normal projected entangled pair states generating the same state
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Tensor-network approach to phase transitions in string-net models
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States
• Wegner-Wilson loops in string nets

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• Entanglement generation in $(1+1)D$ QED scattering processes
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• 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