Fig. 1: Overview of this work.
a The 1D lattice Schwinger model (top) describes quantum electrodynamics on a lattice. Fermionic degrees of freedom ψn on odd (even) sites represent the presence or absence of an electron (positron), while the electric fields Ln reside on the bonds and mediate coupling between the particles. In 1D, one can integrate out the fields and apply a Jordan-Wigner transform, which results in an XY-type model for spins σ = ↑, ↓. The dynamical fields are replaced by static background charges qn, which act as a disorder potential for spins. b Schematic phase diagram for the 1D lattice Schwinger model as a function of the dimensionless coupling ratio J/w [see Eq. (3) for details]. In the weak-coupling limit J/w → 0, the model reduces to an integrable XY spin chain. In the thermodynamic limit, any finite J breaks integrability, resulting in a chaotic phase. Around J/w ~ 1, an ergodicity-breaking transition, consistent with an onset of MBL (many-body localization), has previously been observed56. However, the nature and extent of the MBL phase is difficult to ascertain in finite-size systems due to its proximity to the regime dominated by Hilbert space fragmentation. The latter is exact at J/w → ∞ and, as shown in this paper, strongly affects the properties of numerically-accessible systems even at J/w ~ 5.
