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Register a new userReal Time Dynamics and Confinement in the $mathbb{Z}_{n}$ Schwinger-Weyl lattice model for 1+1 QED
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We study the out-of-equilibrium properties of $1+1$ dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian $mathbb{Z}_{n}$ gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.
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The $mathbb{C}P^{N-1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on $S_{s}^{1} times S_{tau}^{1}$ with radii $L_{s}$ and $L_{tau}$, respectively, where the ratio of the circumferences is taken to be sufficiently large ($L_{s}/L_{tau} gg 1$) to simulate the model on $mathbb{R} times S^1$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as $L_{tau}$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global PSU($N$)=SU($N$)$/{mathbb Z}_{N}$ symmetry remains unbroken at quantum and classical levels for the small and large $L_{tau}$, respectively: in the small $L_tau$ region for finite $N$, the order parameter fluctuates extensively with its expectation value consistent with zero after taking an ensemble average, while in the large $L_tau$ region the order parameter remains small with little fluctuations. We also calculate the thermal entropy and find that the degrees of freedom in the small $L_{tau}$ regime are consistent with $N-1$ free complex scalar fields, thereby indicating a good agreement with the prediction from the large-$N$ study for small $L_{tau}$.
We study the ground-state properties of a class of $mathbb{Z}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the $mathrm{U}(1)$ group, preserve the unitary character of the minimal coupling, and have therefore the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper we study the cases $n = 2 div 8$ by means of a DMRG code that exactly implements Gauss law. We perform a careful scaling analysis, and show that, in absence of a background field, all $mathbb{Z}_n$ models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the $CP$ symmetry. We then perform the large-$n$ limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition the zero-charge sector of the massive Schwinger model, which occurs at negative mass.
We show how to implement a Rydberg-atom quantum simulator to study the non-equilibrium dynamics of an Abelian (1+1)-D lattice gauge theory. The implementation locally codifies the degrees of freedom of a $mathbf{Z}_3$ gauge field, once the matter field is integrated out by means of the Gauss local symmetries. The quantum simulator scheme is based on current available technology and scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, to explore different string dynamics and to infer information about the Schwinger $U(1)$ model.
We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a non-zero electric flux in the initial state can unwind and decrease to a minimum value equal to minus its initial value, due to the effects of a pair of charges that repeatedly traverse the spatial circle. Our numerical results support the existence of this flux unwinding phenomenon, both for initial states containing a charged pair inserted by hand, and when the charges are produced by Schwinger pair production. We also study boundary conditions where charges are confined to an interval and flux unwinding cannot occur, and the massless limit, where our results agree with the predictions of the bosonized description of the Schwinger model.
Kitaevs toric code is an exactly solvable model with $mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for $mathbb{Z}_2$ lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a $pi$-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.
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