Many‐body localization in incommensurate models with a mobility edge

Abstract

We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. A conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions. However, contrary to this intuition there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of such incommensurate models, in the non-interacting limit, shows that they admit extended, partially extended, and fully localized many-body states. Non-interacting incommensurate models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and nonergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called "many-body proximity effect" and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without singleparticle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.

Many-body dynamics in long-range hopping models in the presence of correlated and uncorrelated disorder

“…Moreover, in both sides of a = 1, transition between different P s phases are clearly visible. The volume law of eigenstate EE has also been recently observed for 1D short-range noninteracting model in the presence of correlated disorder, where there exists a mobility edge in single particle spectrum [65,66].…”

Energy Current Rectification and Mobility Edges

“…Localization occurs also for quasi periodic potentials, as the prototypical Aubry-André-Harper model, but only once the magnitude of the potential is larger than a certain threshold value [18,19]. The localizing effects of disordered and quasi-periodic po-tentials, in non-interacting and interacting cases, have been verified experimentally [20][21][22][23][24][25][26][27][28][29][30][31].Systems with a quasi-periodic potential may present mobility edges, which means that there is a particular value of the energy which differentiates energy eigenstates which are localized from delocalized ones [32][33][34][35][36][37][38][39], as recently observed experimentally [40]. The transport properties of systems with mobility edges have been studied before, showing, for example, a transition between ballistic transport to insulating behavior separated by a critical line with subdiffusive transport [41].In this work we consider two identical spin baths of differing temperature connected to the boundaries of a quadratic bosonic chain with a generalized Aubry-André-Harper potential which induces a mobility edge.…”

“…Systems with a quasi-periodic potential may present mobility edges, which means that there is a particular value of the energy which differentiates energy eigenstates which are localized from delocalized ones [32][33][34][35][36][37][38][39], as recently observed experimentally [40]. The transport properties of systems with mobility edges have been studied before, showing, for example, a transition between ballistic transport to insulating behavior separated by a critical line with subdiffusive transport [41].…”

Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

“…Hence, we might expect, naïvely, that single-parameter scaling holds, at least, for this class of 3d quasiperiodic systems. We examine this naïve expectation in detail.Some recent works [13][14][15] have examined open-system transport and closed-system wave-packet dynamics in quasiperiodic chains, described by the Aubry-Andre model [3] and its variants [28,29], and shown that the delocalization-localization critical point exhibits anomalous behavior: An initially localized wave packet spreads diffusively or superdiffusively with time in an isolated arXiv:1810.12931v1 [cond-mat.dis-nn] 30 Oct 2018 2 system, whereas the conductance, at high or infinite temperature, shows subdiffusive scaling with system size, i.e., g ∼ L α with α < −1, for open chains connected, at its ends, to two infinite leads [13,14]. These results indicate quasiperiodic systems have much richer transport properties, at this critical point, than random systems.We carry out a systematic characterization of electronic transport in the quasiperiodic, 1d Aubry-Andre model and in its 2d and 3d generalizations.…”