Tensor Networks for Lattice Gauge Theories with continuous groups

TL;DR

This paper develops a tensor network framework for lattice gauge theories with continuous groups, enabling efficient numerical simulations and new insights into phase transitions and gauge invariance.

Contribution

It introduces a tensor network formulation for lattice gauge theories, providing a variational ansatz, a truncation scheme, and new gauge-invariant operators for phase diagram exploration.

Findings

Characterized the phase transition between Z2 and U(1) gauge theories using entanglement entropy.

Proposed a tensor network approach that captures gauge invariance and microscopic relations.

Extended the phase diagram with new gauge-invariant operators.

Abstract

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge invariant states that can be used in actual numerical computation. Our construction is also applied to the simplest realization of the quantum link models/gauge magnets and provides a clear way to understand their microscopic relation with Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge invariant operators that modify continuously Rokshar-Kivelson wave functions and can be used to extend the phase diagram of known models. As an example we characterize the transition between the deconfined phase of the $Z_2$ lattice gauge theory and the Rokshar-Kivelson point of the U(1) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.