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Register a new userHeat percolation in many-body flatband localizing systems
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Translationally invariant finetuned single-particle lattice Hamiltonians host flat bands only. Suitable short-range many-body interactions result in complete suppression of particle transport due to local constraints and Many-Body Flatband Localization. Heat can still flow between spatially locked charges. We show that heat transport is forbidden in dimension one. In higher dimensions heat transport can be unlocked by tuning filling fractions across a percolation transition for suitable lattice geometries. Transport in percolation clusters is additionally affected by effective bulk disorder and edge scattering induced by the local constraints, which work in favor of arresting the heat flow. We discuss explicit examples in one and two dimensions.
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We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some landmarks within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).
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 $ u$ consistent with numerical studies.
Using numerically exact methods we study transport in an interacting spin chain which for sufficiently strong spatially constant electric field is expected to experience Stark many-body localization. We show that starting from a generic initial state, a spin-excitation remains localized only up to a finite delocalization time, which depends exponentially on the size of the system and the strength of the electric field. This suggests that bona fide Stark many-body localization occurs only in the thermodynamic limit. We also demonstrate that the transient localization in a finite system and for electric fields stronger than the interaction strength can be well approximated by a Magnus expansion up-to times which grow with the electric field strength.
We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and post-quench eigenstates decays {it exponentially} with the system size.
It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in the context of a one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the phenomenology of many-body localization. However, at longer times, all finite wavelength spin polarizations decay in a finite time, independent of system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this long pre-thermal dynamical behavior, intermediate between full localization and diffusion, quasi-many body localization.
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