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.
Bibliographical noteFunding Information:
Patrick Emonts thanks Julian Bender, Jeanne Colbois, Daniel Robaina, Stefan Wessel and Thorsten B. Wahl for fruitful discussions. This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868. Patrick Emonts acknowledges support from the International Max-Planck Research School for Quantum Science and Technology (IMPRS-QST) as well as support by the EU-QUANTERA project Quantum Technologies For Lattice Gauge theories (BMBF Grant No. 13N14780). P. E. thanks the Hebrew University of Jerusalem for the hospitality during his stay at the Racah Institute of Physics.
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