Real-space renormalization group approach to the Anderson model

Abstract

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.

Author Keywords: disorder, localization, real-space renormalization, strong correlations

    Item Description
    Type
    Contributors
    Thesis advisor (ths): Wortis, Rachel
    Degree committee member (dgc): Tamblyn, Isaac
    Degree committee member (dgc): Atkinson, Bill A
    Degree granting institution (dgg): Trent University
    Date Issued
    2017
    Date (Unspecified)
    2017
    Place Published
    Peterborough, ON
    Language
    Extent
    198 pages
    Rights
    Copyright is held by the author, with all rights reserved, unless otherwise noted.
    Subject (Topical)
    Local Identifier
    TC-OPET-10476
    Publisher
    Trent University
    Degree
    Master of Science (M.Sc.): Materials Science