Percolation in Fock space as a proxy for many-body localization

Journal article

We study classical percolation models in Fock space as proxies for the quantum many-body localization (MBL) transition. Percolation rules are defined for two models of disordered quantum spin chains using their microscopic quantum Hamiltonians and the topologies of the associated Fock-space graphs. The percolation transition is revealed by the statistics of Fock-space cluster sizes, obtained by exact enumeration for finite-sized systems. As a function of disorder strength, the typical cluster size shows a transition from a volume law in Fock space to subvolume law, directly analogous to the behavior of eigenstate participation entropies across the MBL transition. Finite-size scaling analyses for several diagnostics of cluster size statistics yield mutually consistent critical properties. We show further that local observables averaged over Fock-space clusters also carry signatures of the transition, with their behavior across it in direct analogy to that of corresponding eigenstate expectation values across the MBL transition. The Fock-space clusters can be explored under a mapping to kinetically constrained models. Dynamics within this framework likewise show the ergodicity-breaking transition via Monte Carlo averaged local observables and yield critical properties consistent with those obtained from both exact cluster enumeration and analytic results derived in our recent work [arXiv:1812.05115]. This mapping allows access to system sizes two orders of magnitude larger than those accessible in exact enumerations. Simple physical pictures based on freezing of local real-space segments of spins are also presented and shown to give values for the critical disorder strength and correlation length exponent ν consistent with numerical studies.

Authors: Roy, S; Chalker, J; Logan, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 99
• Issue: 10
• Article number: 104206
• Publication date: 2019-03-25
• Acceptance date: 2019-03-07
• DOI: 10.1103/PhysRevB.99.104206
• EISSN: 2469-9969
• ISSN: 2469-9950