Vasquez, Louella J. (2010) High precision multifractal analysis in the 3D Anderson model of localisation. PhD thesis, University of Warwick.

Preview

PDF WRAP_THESIS_Vasquez_2010.pdf - Requires a PDF viewer. Download (21Mb)

Request Changes to record.

Abstract

This work presents a large scale multifractal analysis of the electronic state
in the vicinity of the localisation-delocalisation transition in the three-dimensional
Anderson model of localisation using high-precision data and very large system
sizes of up to L3 = 2403. The multifractal analysis is implemented using box- and
system- size scaling of the generalized inverse participation ratios employing typical
and ensemble averaging techniques. The statistical analysis in this study has shown
that in the thermodynamic limit a proposed symmetry relation in the multifractal
exponents is true for the 3D Anderson model in the orthogonal universality class.
Better agreement with the symmetry is found when using system-size scaling with
ensemble averaging in which a more complete picture of the multifractal spectrum
f(α) is also obtained. A complete profile of f(α) has negative fractal dimensions
and shows the contributions coming from the tails of the distribution. Various boxpartitioning
approaches have been carefully studied such as the use of cubic and
non-cubic boxes, periodic boundary conditions to enlarge the system, and single
and multiple origins in the partitioning grid. The most reliable method is equal
partitioning of a system into cubic boxes which has also been shown to be the least
numerically expensive. Furthermore, this work gives an expression relating f(α)
and the probability density function (PDF) of wavefunction intensities. The relation
which contains a finite-size correction provides an alternative and simpler method
to obtain f(α) directly from the PDF in which f(α) is interpreted as the scaleinvariant
distribution at criticality. Finally, a generalization of standard multifractal
analysis which is applicable to the critical regime and not just at the critical point is
presented here. Using this generalization together with finite-size scaling analysis,
estimates of critical disorder and critical exponent based on exact diagonalization
have been obtained that are in excellent agreement, supporting for the first time
previous results of transfer matrix calculations.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Anderson model, Multifractals
Official Date:	July 2010
Dates:	Date Event July 2010 Submitted
Institution:	University of Warwick
Theses Department:	Department of Physics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Römer, Rudolf ; Rodriguez, Alberto
Sponsors:	University of Warwick ; Engineering and Physical Sciences Research Council (EPSRC) (EP/C007042/1) ; Ōsaka Daigaku [Osaka University]
Extent:	xii, 117 p. : ill., charts
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads