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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• Estimating the central charge from the Rényi entanglement entropy
• Reweighting Lefschetz Thimbles
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• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources
• Lattice Hamiltonian approach to the massless Schwinger model: precise extraction of the mass gap
• Phase structure of two-dimensional QED at zero temperature with flavor-dependent chemical potentials and the role of multidimensional theta functions
• Developing and testing the density of states FFA method in the SU(3) spin model
• Abelian and non-abelian symmetries in infinite projected entangled pair states
• Two flavor massless Schwinger model on a torus at a finite chemical potential
• Lefschetz thimbles in fermionic effective models with repulsive vector-field
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• Modifying partition functions: a way to solve the sign problem
• Zeta-regularized vacuum expectation values
• Tensor renormalization group in bosonic field theory
• Equation of state for cold and dense heavy QCD
• Topological phases of lattice bosons with a dynamical gauge field
• Complex Langevin Simulations of QCD at Finite Density -- Progress Report
• Beyond complex Langevin equations II: a positive representation of Feynman path integrals directly in the Minkowski time
• Topological Defects in Quantum Field Theory with Matrix Product States
• Towards a theoretical description of dense QCD
• Positive Representations of a Class of Complex Measures
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Anatomy of a strong residual sign problem on the thimbles
• New techniques and results for worldline simulations of lattice field theories
• Efficient approximation for global functions of matrix product operators

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• Topological chiral currents in the Gross-Neveu model extension
• Fermionic wave packet scattering: a quantum computing approach
• Quantum thermodynamics of nonequilibrium processes in lattice gauge theories
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Evolution Operator Can Always be Separated into the Product of Holonomy and Dynamic Operators
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Towards a nonperturbative construction of the $S$-matrix
• Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model
• The phase diagram of quantum chromodynamics in one dimension on a quantum computer
• Hybrid Tree Tensor Networks for quantum simulation
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Density of States of the lattice Schwinger model
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• Truly Lorentzian quantum cosmology
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Entanglement renormalization for gauge invariant quantum fields
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Chiral fermion in the Hamiltonian lattice gauge theory
• A quantum information perspective on meson melting
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• The rotor Jackiw-Rebbi model: a cold-atom approach to chiral symmetry restoration and quark confinement
• Fractal states of the Schwinger model
• A single-particle framework for unitary lattice gauge theory in discrete time
• Towards Quantum Simulating Non-Abelian Gauge Theories
• Meson thermalization with a hot medium in the open Schwinger model
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Spectroscopy with the tensor renormalization group method
• Internal structure of gauge-invariant Projected Entangled Pair States
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Detecting spacelike vacuum entanglement at all distances and promoting negativity to a necessary and sufficient entanglement measure in many-body regimes
• Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
• Quantum phase diagram for two species hardcore bosons in one-dimensional optical lattices with the resonantly driven Rabi frequency
• The Cytnx Library for Tensor Networks
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Heavy Quarkonium at finite temperature and chemical potential
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• On Strongly Coupled Matrix Theory and Stochastic Quantization: A New Approach to Holographic Dualities
• Engineering a Josephson junction chain for the simulation of the clock model
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Landau-Zener-Stückelberg-Majorana dynamics of magnetized quarkonia
• Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method
• Digital Quantum Simulation of Hadronization in Yang-Mills Theory
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
• Real-space blocking of qubit variables on parallel lattice gauge theory links for quantum simulation
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Higher-order structure of Hamiltonian truncation effective theory
• Particle-Number Threshold for Non-Abelian Geometric Phases