Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a $U(1)$ gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for $\mathrm{U}(N)$ and $\mathrm{SU}(N)$ lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.

The momentum diffusion coefficient for heavy quarks is studied in a deconfined gluon plasma in the static approximation by investigating a correlation function of the color electric field using Monte~Carlo techniques. The diffusion coefficient is extracted from the long-distance behavior of such a correlator. For temperatures Tc<T$\lesssim${}2Tc, our nonperturbative estimate of the diffusion coefficient is found to be very different from the leading-order perturbation theory and is in the right ballpark to explain the heavy quark flow seen by the PHENIX Collaboration at the RHIC experiment.

We consider the spectrum of a $U(1)$ quantum link model where gauge fields are realized as $S=1/2$ spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian $H={\mathcal{O}}_{\mathrm{kin}}+\lambda {\mathcal{O}}_{\mathrm{pot}}$, where ${\mathcal{O}}_{\mathrm{pot}}$ (${\mathcal{O}}_{\mathrm{kin}}$) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at $\lambda =0$ whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero $\lambda$ but some special linear combinations that simultaneously diagonalize ${\mathcal{O}}_{\mathrm{kin}}$ and ${\mathcal{O}}_{\mathrm{pot}}$ survive as quantum many-body scars, suggesting an “order-by-disorder” mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.

We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$ universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global $U(1)$ charge can be obtained via a series expansion in the inverse charge $1/Q$. We find that the conformal dimensions of the lowest operator with a fixed charge $Q$ are almost entirely determined by the first few terms in the series.

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-$\frac{1}{2}$ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for $S>\frac{1}{2}$ since such theories converge to the lattice Schwinger model in the large-$S$ limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-$S\mathrm{U}\left(1\right)$ quantum link models (QLMs) with staggered fermions. We find that QMBS persist at $S>\frac{1}{2}$, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial product states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-$S$ QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.