Variational Monte Carlo simulation with tensor networks of a pure Z3 gauge theory in (2+1) D VARIATIONAL MONTE CARLO SIMULATION with TENSOR ... EMONTS, BAÑULS, CIRAC, and ZOHAR

Patrick Emonts, Mari Carmen Bañuls, Ignacio Cirac, Erez Zohar

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Abstract

Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar and J. I. Cirac, Phys. Rev. D 97, 034510 (2018)PRVDAQ2470-001010.1103/PhysRevD.97.034510] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge Kogut-Susskind Hamiltonian with a Z3 gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.

Original languageAmerican English
Article number074501
JournalPhysical Review D
Volume102
Issue number7
DOIs
StatePublished - Oct 2020

Bibliographical note

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© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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