Integrals of motion for onedimensional Anderson localized systems
Anderson localization is known to be inevitable in onedimension 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. Weanswer 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 Type1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction.Wenote that these models can be viewed as disordered electron models with infiniterange hopping, where a similar series truncates at the linear order.Weshow that despite the infinite range hopping, all states but one are localized.Wealso 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.Weformulate 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 welldefinedmore »
 Authors:

^{[1]};
^{[1]};
^{[2]};
^{[3]}
 Indian Institute of Science, Bangalore (India)
 Rutgers Univ., Piscataway, NJ (United States)
 Univ. of California, Santa Cruz, CA (United States)
 Publication Date:
 Grant/Contract Number:
 FG0206ER46319
 Type:
 Accepted Manuscript
 Journal Name:
 New Journal of Physics
 Additional Journal Information:
 Journal Volume: 18; Journal Issue: 3; Journal ID: ISSN 13672630
 Publisher:
 IOP Publishing
 Research Org:
 Univ. of California, Santa Cruz, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Anderson localization; integrals of motion; localization–delocalization transition
 OSTI Identifier:
 1255231
Modak, Ranjan, Mukerjee, Subroto, Yuzbashyan, Emil A., and Shastry, B. Sriram. Integrals of motion for onedimensional Anderson localized systems. United States: N. p.,
Web. doi:10.1088/13672630/18/3/033010.
Modak, Ranjan, Mukerjee, Subroto, Yuzbashyan, Emil A., & Shastry, B. Sriram. Integrals of motion for onedimensional Anderson localized systems. United States. doi:10.1088/13672630/18/3/033010.
Modak, Ranjan, Mukerjee, Subroto, Yuzbashyan, Emil A., and Shastry, B. Sriram. 2016.
"Integrals of motion for onedimensional Anderson localized systems". United States.
doi:10.1088/13672630/18/3/033010. https://www.osti.gov/servlets/purl/1255231.
@article{osti_1255231,
title = {Integrals of motion for onedimensional Anderson localized systems},
author = {Modak, Ranjan and Mukerjee, Subroto and Yuzbashyan, Emil A. and Shastry, B. Sriram},
abstractNote = {Anderson localization is known to be inevitable in onedimension 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. Weanswer 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 Type1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction.Wenote that these models can be viewed as disordered electron models with infiniterange hopping, where a similar series truncates at the linear order.Weshow that despite the infinite range hopping, all states but one are localized.Wealso 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.Weformulate 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 welldefined in localized phase, but not so in the extended phase. Lastly, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.},
doi = {10.1088/13672630/18/3/033010},
journal = {New Journal of Physics},
number = 3,
volume = 18,
place = {United States},
year = {2016},
month = {3}
}