Fock-space fragmentation in quenches of disordered interacting fermions

arXiv:2510.19510v2 Announce Type: replace-cross Abstract: Fock-space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to non-ergodic dynamics and possible breakdown of the eigenstate thermalization hypothesis. Here, we demonstrate that also in disordered systems, such as the XXZ model with random on-site fields, fragmentation appears as a natural concept offering fresh perspectives, for example, on many-body localization (MBL). Specifically, for a given quenched initial state, we identify a potential-energy shell in Fock space, defined by its energy and energy uncertainty, which represents the energetically accessible part of the many-body configuration space. For example, the drastic sample-to-sample fluctuations observed in the weak disorder regime, $W<W_{\mathrm{frag}}$, represent fluctuations of the mass of the shell. Upon increasing disorder, the potential-energy shell becomes increasingly fragmented. Its finite-size evolution exhibits a turnaround flow; extrapolating this flow to the disorder at which the turnaround vanishes provides a heuristic estimate of the strong-fragmentation scale $W_{\mathrm{frag}}$. We conjecture that the fragmentation identified here provides a geometric mechanism contributing to the finite-time slowing down of relaxation observed in studies of disordered interacting systems.

Abstract:Fock-space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to non-ergodic dynamics and possible breakdown of the eigenstate thermalization hypothesis. Here, we demonstrate that also in disordered systems, such as the XXZ model with random on-site fields, fragmentation appears as a natural concept offering fresh perspectives, for example, on many-body localization (MBL). Specifically, for a given quenched initial state, we identify a potential-energy shell in Fock space, defined by its energy and energy uncertainty, which represents the energetically accessible part of the many-body configuration space. For example, the drastic sample-to-sample fluctuations observed in the weak disorder regime, $W<W_{\mathrm{frag}}$, represent fluctuations of the mass of the shell. Upon increasing disorder, the potential-energy shell becomes increasingly fragmented. Its finite-size evolution exhibits a turnaround flow; extrapolating this flow to the disorder at which the turnaround vanishes provides a heuristic estimate of the strong-fragmentation scale $W_{\mathrm{frag}}$. We conjecture that the fragmentation identified here provides a geometric mechanism contributing to the finite-time slowing down of relaxation observed in studies of disordered interacting systems.

Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2510.19510 [cond-mat.dis-nn]

(or arXiv:2510.19510v2 [cond-mat.dis-nn] for this version)

Phys. Rev. Research 8, 043030 (2026)

https://doi.org/10.1103/hvqr-6n3b DOI(s) linking to related resources

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Fock-space fragmentation in quenches of disordered interacting fermions

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