Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge 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, 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.

arXiv comment13 pages, 7 figures; v2: as published

References in corpus (20)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The phase diagram of dense QCD
• Renormalization and tensor product states in spin chains and lattices
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Wave function optimization in the variational Monte Carlo method
• Review on novel methods for lattice gauge theories
• Variational quantum Monte Carlo simulations with tensor-network states
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Entanglement renormalization and gauge symmetry
• Breakdown of a perturbed Z_N topological phase
• Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
• Building Projected Entangled Pair States with a Local Gauge Symmetry
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories

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