Wilson loops and area laws in lattice gauge theory tensor networks

Erez Zohar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 too - lattice gauge theories. In order to extract physical properties (such as expectation values and correlation functions of physical observables) out of such states, one has to use the so-called transfer operators, the local properties of which dictate the long-range behavior of the state. In this paper we study transfer operators of tensor network states (in particular, projected entangled pair states) of lattice gauge theories, and consider the implications of the local symmetry on their structure and properties. In particular, we study the implications on the computation of the Wilson loop - a nonlocal, gauge-invariant observable which is central to pure gauge theories, the long-range decay behavior of which probes the confinement or deconfinement of static charges. Using the symmetry, we show how to simplify the tensor contraction required for computing Wilson loop expectation values for such states, eliminate nonphysical parts of the tensors, and formulate conditions relating local properties (that is, of the tensors) to their decay fashion.

Original languageAmerican English
Article number033179
JournalPhysical Review Research
Volume3
Issue number3
DOIs
StatePublished - Sep 2021

Bibliographical note

Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

Fingerprint

Dive into the research topics of 'Wilson loops and area laws in lattice gauge theory tensor networks'. Together they form a unique fingerprint.

Cite this