Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap

TL;DR

This paper reviews tensor network methods for lattice gauge theories beyond one dimension, highlighting their advantages over Monte Carlo methods and proposing a roadmap for future algorithmic development to address high-energy physics challenges.

Contribution

It provides a comprehensive review of current tensor network techniques and outlines a strategic plan to improve their scalability and applicability to complex high-energy physics problems.

Findings

Tensor networks avoid the sign problem in lattice gauge theories.

Estimated resource scaling for large-scale computations is provided.

Roadmap for algorithmic improvements in tensor network methods is proposed.

Abstract

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories approaching relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. In this work, we review the state-of-the-art of Tensor Network methods and discuss a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.