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

• URL: http://arxiv.org/abs/2008.00882v2
• Date: Fri, 9 Oct 2020 09:26:05 GMT
• Title: Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d
• Authors: Patrick Emonts, Mari Carmen Ba\~nuls, J. Ignacio Cirac, Erez Zohar
• Abstract summary: Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. It is possible to efficiently compute physical observables using a variational Monte Carlo procedure. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters.
• Score: 0.688204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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