Percolation in Fock space as a proxy for many-body localisation
Physical review B: Condensed matter and materials physics American Physical Society
Abstract:
We study classical percolation models in Fock space as proxies for the quantum many-body localisation (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 sub-volume law, directly analogous to the behaviour 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 behaviour 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 $\nu$ consistent with numerical studies.Phenotype bias determines how natural RNA structures occupy the morphospace of all possible shapes
Pole skipping from universal hydrodynamics of (1+1)d QFTs
https://arxiv.org/abs/2512.11024
Abstract:
(1+1)d QFTs provide a tractable arena for understanding the emergence of hydrodynamics in thermal states. At high temperatures this process is governed by the weak breaking of conformal symmetry, and so in this limit many features of the hydrodynamic theory that emerges have been argued to be universal. In this paper we study aspects of the stress tensor thermal two-point function in holographic QFTs of this kind and show that they are consistent with the universal hydrodynamic theory proposed to apply at late times. Specifically, we identify the locations of the `pole skipping' points in momentum space at which there is an intersection of poles and zeroes of this two-point function in holographic QFTs. Although these points lie outside the regime where the hydrodynamic theory is controlled, we show that their locations are consistent with those found by resumming the hydrodynamic derivative expansion near the lightcone. For example, this resummation of the universal hydrodynamics correctly predicts the butterfly velocity of holographic theories.