Fig. 3: Experimental probes.
We analyze several observables that could be probed experimentally. a, b show results from ED simulations of the time-evolution of the microscopic model (3) with experimentally realistic parameters in a system with coordination number z = 3 (see inset). In (a) we observe disorder-free localization by initializing the system in a gauge-invariant (blue curve) and gauge-noninvariant (red curve) initial state with two matter excitations localized in subsystem A and calculating the time-averaged imbalance between subsystem A and B as shown. In (b), we probe the Schwinger effect by quenching the vacuum state with the microscopic model for different experimentally relevant parameters: matter detuning Δm (chemical potential) and link detuning Δl (electric field). We find lines of resonance, where the production of matter excitations out of the vacuum is large. In (c), we plot the average U(1) matter density (blue curve) obtained from DMRG calculations on a ladder with J < 0. We can qualitatively understand the sharp decay of matter as a transition into the vacuum phase as discussed in Fig. 2a. Additionally, a kink in the plaquette expectation value (red curve) signals a phase transition. In (d), we use two fluctuating test charges to probe a temperature-induced deconfinement transition in a classical limit of our effective model using Monte Carlo simulations. Both in the percolation strength (red curve) and the Euclidean distance of two matter excitations (blue curve), we find that above a certain temperature T/h the system undergoes a percolation transition.
