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Register a new userQuantum simulation of lattice gauge theories using Wilson fermions
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Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.
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We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and 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 non-zero 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.
We discuss a general framework for the realization of a family of abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable to quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions originally proposed by Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4x4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices where we discuss in detail a protocol for the preparation of the ground state. We also comment on the relation between standard compact U(1) LGT and the model considered.
We describe the simulation of dihedral gauge theories on digital quantum computers. The nonabelian discrete gauge group $D_N$ -- the dihedral group -- serves as an approximation to $U(1)timesmathbb{Z}_2$ lattice gauge theory. In order to carry out such a lattice simulation, we detail the construction of efficient quantum circuits to realize basic primitives including the nonabelian Fourier transform over $D_N$, the trace operation, and the group multiplication and inversion operations. For each case the required quantum resources scale linearly or as low-degree polynomials in $n=log N$. We experimentally benchmark our gates on the Rigetti Aspen-9 quantum processor for the case of $D_4$. The fidelity of all $D_4$ gates was found to exceed $80%$.
In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultra-cold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly-correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.
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