Fate of many-body localization in an Abelian lattice gauge theory

We address the fate of many-body localization (MBL) of mid-spectrum eigenstates of a matter-free $U(1)$ quantum-link gauge theory Hamiltonian with random couplings on ladder geometries. We specifically consider an intensive estimator, D ∈ [0,1/4], that acts as a measure of elementary plaquettes on the lattice being active or inert in mid-spectrum eigenstates as well as the concentration of these eigenstates in Fock space, with D being equal to its maximum value of $1/4$ for Fock states in the electric flux basis. We calculate its distribution, p(D), for Lₓ × Ly lattices, with Ly=2 and $4$, as a function of (a dimensionless) disorder strength α (α=0 implies zero disorder) using exact diagonalization on many disorder realizations. Analyzing the skewness of p(D) shows that the finite-size estimate of the critical disorder strength, beyond which MBL sets in for thin ladders with Ly=2, increases linearly with Lₓ while the behavior of the full distribution with increasing Lₓ at fixed α shows that αc (Ly=2) >40, if at all finite, based on data for Lₓ ≤ 12. p(D) for wider ladders with Ly=4 show their lower tendency to localize, suggesting a lack of MBL in two dimensions. A remarkable observation is the resolution of the (monotonic) infinite temperature autocorrelation function of single plaquette diagonal operators in typical high-energy Fock states into a plethora of emergent timescales of increasing spatio-temporal heterogeneity as the disorder is increased even before MBL sets in. At intermediate and large α, but below αc (Ly), certain randomly selected initial Fock states display striking oscillatory temporal behavior of such plaquette operators dominated by only a few frequencies, reminiscent of oscillations induced by quantum many-body scars.