Variational Monte Carlo Simulation with Tensor Networks of a Pure $Z_3$ Gauge Theory in $( 2 + 1 )$ D


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)] 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 KogutSusskind 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.

American Physical Society (APS)