Disorder can have a vast variety of consequences for the physics of phase transitions. Some transitions remain unchanged in the presence of disorder while others are completely
destroyed. In this dissertation we study the effects of quenched disorder on electronic systmens at zero temperature. First, we perform variational studies of the interaction-localization
problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling
studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized
even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g* signaling the crossover to
strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations
of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects. Second, we formulate a
strong-disorder renormalization-group (SDRG) approach to study the beta function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the
band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The beta function is shown
to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this
particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the beta function is shown to crossover from the universal behavior of the
particle-hole symmetric case to the conventional nonuniversal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising
chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model, while the generic case corresponds to the Griffiths
paramagnetic phase. Finally, we implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-
Renyi random graphs, which represent an appropriate infinite dimensional limit. Our SDRG algorithm is based on a judicious elimination of most (irrelevant) new bonds generated under RG. It
yields excellent agreement with exact numerical results for universal properties at the critical point without significant increase of computer time, and confirm that, for Anderson
localization, the upper critical dimension duc = infinite. We find excellent convergence of the relevant 1/d expansion down to d = 2, in contrast to the conventional 2 + ε
expansion, which has little to say about what happens in any d [greater than] 3. We show that the mysterious mirror symmetry of the conductance scaling function is a genuine strong-coupling effect,
as speculated in early work. This opens an efficient avenue to explore the critical properties of Anderson transition in the strong-coupling limit in high dimensions. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / November 4, 2015. / Anderson transition, disordered systems, finite size scaling, random, Renormalziation Group, SDRG / Includes bibliographical references. / Vladimir Dobrosavljević, Professor Directing Dissertation; Vincent J. M. Salters, University Representative; Stephan von Molnar, Committee Member; Kun
Yang, Committee Member; Jorge Piekarewicz, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_291302 |
| Contributors | Javan Mard, Hossein (authoraut), Dobrosavljević, Vladimir (professor directing dissertation), Salters, Vincent J. M. (university representative), Von Molnar, S. (Stephan), 1935- (committee member), Yang, Kun, 1967- (committee member), Piekarewicz, Jorge, 1956- (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Physics (degree granting department) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (119 pages), computer, application/pdf |
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