Review on novel methods for lattice gauge theories

Abstract

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

28 pages (including 15 figures) plus bibliography. Comments are most welcome

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• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
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• Tensor renormalization group study of the 3d $O(2)$ model
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• Quantum Computation of Phase Transition in the Massive Schwinger Model
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• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• A Cold-Atom Particle Collider
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• Synthetic Flux Attachment
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• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
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• Disorder-free localization with Stark gauge protection
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• First-Order Phase Transition of the Schwinger Model with a Quantum Computer
• Breaking of the gauge symmetry in lattice gauge theories
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
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• Quantum Computation of the Massive Thirring Model
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