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.

Empirical Consequences of Emergent Mass

“…On the other hand, if a reductive approach is possible, then non-perturbative calculational methods must be developed to define and solve QCD. Prominent amongst such techniques today are (i) the numerical simulation of lQCD [74][75][76] and (ii) continuum Schwinger function methods (CSMs), viz.ã collection of models and schemes, each with varying degrees of connection to Equation (2). Currently, each of these two approaches has strengths and weaknesses, so the best way forward is to combine them to the fullest extent that is reasonably possible and exploit the synergies that emerge.…”

Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

“…The arrival of functional quantum devices [20] thus creates an urgent need for a thorough grasp of Hamiltonian lattice gauge theory and how its structure can be related to that of quantum architectures. Several attempts at making proposals for quantum-simulating lattice gauge theories have been made in recent years [17,21,22]. Most of the attempts thus far have been for simpler models like Z 2 gauge theories [17,23,24] or U(1) gauge theories in 1 þ 1 dimensions [25][26][27][28], including the first digital quantum simulation of the Schwinger model on a small lattice [29].…”

Synthetic flux attachment

“…Thus, great effort is currently being put in giving dynamics to synthetic gauge potentials [36,37]. The usual top-down approach [38][39][40], using the Kogut-Susskind formalism [41] and quantum link models [42], builds on the knowledge gathered from lattice gauge theories [43].…”