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arXiv · 2008.00882

Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d

Patrick Emonts·Mari Carmen Bañuls·J. 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, J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] 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 $\mathbb{Z}_3$ 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.

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Patrick Emonts, Mari Carmen Bañuls, J. Ignacio Cirac, Erez Zohar. 2020-08-03. Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d. https://doi.org/10.1103/physrevd.102.074501

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