Many-body localization in incommensurate models with a mobility edge

Deng, Dong-Ling and Ganeshan, Sriram and Li, Xiaopeng and Modak, Ranjan and Mukerjee, Subroto and Pixley, JH (2017) Many-body localization in incommensurate models with a mobility edge. In: ANNALEN DER PHYSIK, 529 (7).

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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 non-ergodicity 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 single-particle 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.

Item Type:	Editorials/Short Communications
Publication:	ANNALEN DER PHYSIK
Additional Information:	Copy right for this article belongs to the WILEY-V C H VERLAG GMBH, POSTFACH 101161, 69451 WEINHEIM, GERMANY
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	23 Dec 2017 08:57
Last Modified:	23 Dec 2017 08:57
URI:	http://eprints.iisc.ac.in/id/eprint/58486

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