Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories

TL;DR

This paper introduces gauged Gaussian PEPS, a tensor network-based variational method for simulating lattice gauge theories that overcomes sign problems and can handle real-time dynamics and fermionic matter.

Contribution

It develops a comprehensive framework for gauged Gaussian PEPS, enabling efficient, sign-problem-free simulations of non-perturbative gauge theories in any dimension.

Findings

Efficient evaluation of gauged Gaussian PEPS in multiple dimensions.

Applicable to arbitrary gauge groups and includes fermionic matter.

Provides a new variational approach for real-time dynamics in gauge theories.

Abstract

Gauge theories form the basis of our understanding of modern physics - ranging from the description of quarks and gluons to effective models in condensed matter physics. In the non-perturbative regime, gauge theories are conventionally treated discretely as lattice gauge theories. The resulting systems are evaluated with path-integral based Monte Carlo methods. These methods, however, can suffer from the sign problem and do not allow for a direct evaluation of real-time dynamics. In this work, we present a unified and comprehensive framework for gauged Gaussian Projected Entangled Pair States (PEPS), a variational ansatz based on tensor networks. We review the construction of Hamiltonian lattice gauge theories, explain their similarities with PEPS, and detail the construction of the state. The estimation of ground states is based on a variational Monte Carlo procedure with the PEPS as an ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any dimension with arbitrary gauge groups, and can include dynamical fermionic matter, suggesting new options for the simulation of non-perturbative regimes of gauge theories, including QCD.