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Integrals of motion for one-dimensional Anderson localized systems

Modak, Ranjan and Mukerjee, Subroto and Yuzbashyan, Emil A and Shastry, Sriram B (2016) Integrals of motion for one-dimensional Anderson localized systems. In: NEW JOURNAL OF PHYSICS, 18 .

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Official URL: http://dx.doi.org/10.1088/1367-2630/18/3/033010

Abstract

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the IOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Keywords: Anderson localization; integrals of motion; localization-delocalization transition
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Depositing User: Id for Latest eprints
Date Deposited: 12 May 2016 07:42
Last Modified: 29 Oct 2018 15:33
URI: http://eprints.iisc.ac.in/id/eprint/53791

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