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Lattice gauge theories are a fascinating and rich class of theories relating to the most fundamental models of particle physics, and as experimental control on the quantum level increases there is a growing interest in non-equilibrium…
Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a…
The goal of this article is to review developments regarding the use of ultra-cold atoms as quantum simulators. Special emphasis is placed on relativistic quantum phenomena, which are presumably most interesting for the audience of this…
To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories,…
Lattice gauge theories (LGTs) represent one of the most ambitious goals of quantum simulation. From a practical implementation perspective, non-Abelian theories present significantly tougher challenges than Abelian LGTs. However, it is…
Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this…
The quantum link~\cite{Brower:1997ha} Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…
We discuss the experimental engineering of model systems for the description of QED in one spatial dimension via a mixture of bosonic $^{23}$Na and fermionic $^6$Li atoms. The local gauge symmetry is realized in an optical superlattice,…
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative…
The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including…
We have continued our systematic investigations of the numerical simulations of lattice gauge theories in the dual formulation. These include: i) a more practical implementation of the quasi-local updating technique, ii) a thorough…
Quantum link models (QLMs) offer the realistic prospect for the practical implementation of lattice quantum electrodynamics (QED) on modern quantum simulators, and they provide a venue for exploring various nonergodic phenomena relevant to…
Quantum simulation is one of the major applications of quantum devices. In the noisy intermediate-scale quantum era, however, the general quantum simulation is not yet feasible, such as that of lattice gauge theories, which is likely…
The perspectives of numerical simulations in supersymmetric quantum field theories with vector-like gauge symmetries are discussed. A numerical simulation algorithm for SU(2) gauge theory with gluinos is studied and the first results on the…
Quantum simulations of lattice gauge theories offer the potential to directly study the non-perturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large $N_c$ expansions…
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as…
The vacuum dynamics of SU(2) and SU(3) lattice gauge theories is studied by means of a gauge-invariant effective action defined using the lattice Schr\"odinger functional at finite temperature. In the case of the SU(3) gauge theory…
Gauge theories describe the fundamental forces in the standard model of particle physics and play an important role in condensed matter physics. The constituents of gauge theories, for example charged matter and electric gauge field, are…
We demonstrate a novel experimental arrangement which rotates a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated…