skip to main content

SciTech ConnectSciTech Connect

Title: Integrals of motion for one-dimensional Anderson localized systems

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. 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 Type-1 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 infinite-range 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 well-definedmore » 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.« less
 [1] ;  [1] ;  [2] ;  [3]
  1. Indian Institute of Science, Bangalore (India)
  2. Rutgers Univ., Piscataway, NJ (United States)
  3. Univ. of California, Santa Cruz, CA (United States)
Publication Date:
OSTI Identifier:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 18; Journal Issue: 3; Journal ID: ISSN 1367-2630
IOP Publishing
Research Org:
Univ. of California, Santa Cruz, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Anderson localization; integrals of motion; localization–delocalization transition