Variational Monte Carlo simulation with tensor networks of a pureZ3gauge theory in(2+1)D

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)] 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 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.

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

“…As tailored many-body quantum state ansätze, TNs are an efficient approximate entanglement-based representation of physical states, capable of efficiently describe equilibrium properties and real-time dynamics of systems described by complex actions, where Monte Carlo simulations fail to efficiently converge 22 . TN methods have proven remarkable success in simulating LGTs in (1+1) dimensions [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] , and very recently they have shown potential in (2+1) dimensions [42][43][44][45][46][47][48][49][50] . To date, due to the lack of efficient numerical algorithms to describe high-dimensional systems via TNs, no results are available regarding the realistic scenario of LGTs in three spatial dimensions.…”

Loop-free tensor networks for high-energy physics

“…This framework has led to the development of some of the most successful numerical methods for non-integrable lattice systems, including HEP problems: from DMRG [3,8,37,60] to the time-evolved-block decimation [61,62] and the time-dependent variational principle [63], which are based on the matrix product state ansatz class [6,7], to the tensor renormalization group [64], which is a contraction method for infinite projected entangled pair states (PEPS) [9] and similarly enables the (approximate) calculation of lattice path integrals required in Lagrangian HEP problems [65,66]. TNs are also a physically meaningful ansatz in the context of variational Monte Carlo methods [67], thus providing yet another pathway to study lattice gauge models in higher dimension [68,69]. Hereafter, we concentrate on loop-free TN, i.e.…”

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

“…In this respect, the simplest generalization is provided by Z n LGTs (see, for instance [51][52][53][54][55][56][57][58]). In this case, a gauge degree of freedom is encoded into an n-dimensional Hilbert space, as common in quantum clock models with Z n symmetries [59,60].…”