Disordered Strongly Correlated Electronic Systems

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.