Simulating 2+1d $\mathbb{Z}_3$ lattice gauge theory with iPEPS

TL;DR

This paper demonstrates the simulation of a 2+1 dimensional $ ext{Z}_3$ lattice gauge theory at zero temperature using iPEPS, revealing phase transitions and confinement with efficient algorithms in the thermodynamic limit.

Contribution

It introduces a novel update strategy for iPEPS that efficiently incorporates plaquette terms and Gauss-law constraints in simulating lattice gauge theories.

Findings

Identification of two distinct phases separated by a phase transition.

Evidence of a confined phase through Wilson loop calculations.

Low computational cost reproduces key features of gauge theories.

Abstract

We simulate a zero-temperature pure $\mathbb{Z}_3$ Lattice Gauge Theory in 2+1 dimensions by using an iPEPS (Infinite Projected Entangled-Pair State) ansatz for the ground state. Our results are therefore directly valid in the thermodynamic limit. They clearly show two distinct phases separated by a phase transition. We introduce an update strategy that enables plaquette terms and Gauss-law constraints to be applied as sequences of two-body operators. This allows the use of the most up-to-date iPEPS algorithms. From the calculation of spatial Wilson loops we are able to prove the existence of a confined phase. We show that with relatively low computational cost it is possible to reproduce crucial features of gauge theories. We expect that the strategy allows the extension of iPEPS studies to more general LGTs.