Abstract
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. Apart from level spacing distribution indicators like disorder-averaged mean level spacing, we also consider an intensive estimator D ∈ [0,1/4], which acts as a measure of elementary plaquettes on the lattice that are active or inert in mid-spectrum eigenstates as well as the concentration of these eigenstates in Fock space, with D equal to its maximum value of 1/4 for Fock states in the electric flux basis. We calculate its distribution, p(D), for L_x × L_y lattices, with L_y=2 and 4, as a function of (a dimensionless) disorder strength α (α=0 implies zero disorder) using exact diagonalization in many disorder realizations. Although finite-size estimators based on level spacings do not give a reliable critical disorder strength, α_c(L_y), beyond which MBL prevails as L_x → ∞; a different estimator based on the skewness of p(D) gives α_c(L_y=2)=31.04 ± 0.54 using data for L_x ≤ 14 due to faster convergence. p(D) for wider ladders with L_y=4 show a 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. At intermediate α as well as for α slightly below α_c (L_y), a fraction of randomly selected initial Fock states display striking oscillatory temporal behavior of such plaquette operators in spatial regions formed out of connected plaquettes.