Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model

Lattice gauge theories, the discretized cousins of continuum gauge theories, have become an important platform for the exploration of non-equilibrium phenomena beyond their original scope in the Standard Model. In particular, recent works have reported the possibility of disorder-free localization in the lattice Schwinger model. Using degenerate perturbation theory and numerical simulations based on exact diagonalization and matrix product states, we perform a detailed characterization of thermalization breakdown in the Schwinger model including its spectral properties, the structure of eigenstates, and out-of-equilibrium quench dynamics. We scrutinize the strong-coupling limit of the model, in which an intriguing, double-logarithmic-in-time, growth of entanglement was previously proposed from the initial vacuum state. We identify the origin of this ultraslow growth of entanglement as due to an approximate Hilbert space fragmentation and the emergence of a dynamical constraint on particle hopping, which gives rise to sharp jumps in the entanglement entropy dynamics within individual background charge sectors. Based on the statistics of jump times, we argue that the entanglement growth, averaged over charge sectors, is more naturally explained as either single-logarithmic or a weak power law in time. Our results thus suggest the existence of a single ergodicity-breaking regime due to Hilbert space fragmentation, whose properties are reminiscent of conventional many-body localization within the numerically accessible system sizes.