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

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 $\mathcal{D} \in [0,1/4]$, 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 $\mathcal{D}$ equal to its maximum value of $1/4$ for Fock states in the electric flux basis. We calculate its distribution, $p(\mathcal{D})$, for $L_x \times L_y$ lattices, with $L_y=2$ and $4$, as a function of (a dimensionless) disorder strength $\alpha$ ($\alpha=0$ 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, $\alpha_c(L_y)$, beyond which MBL prevails as $L_x \rightarrow \infty$; a different estimator based on the skewness of $p(\mathcal{D})$ gives $\alpha_c(L_y=2)=31.04 \pm 0.54$ using data for $L_x \leq 14$ due to faster convergence. $p(\mathcal{D})$ 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 $\alpha$ as well as for $\alpha$ slightly below $\alpha_c (L_y)$, 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.