Renormalization-group theory of correlated electron systems

Abstract

The thesis applies position-space renormalization-group theory to a variety of correlated electron systems, determining finite-temperature phase diagrams and thermodynamic properties for electron densities both at and away from half-filling. We begin by assessing the effectiveness of the Suzuki-Takano quantum decimation method on a d = 1 Hubbard model in an external magnetic field, where exact results for the specific heat, magnetic and charge susceptibilities are available at various electron densities. We find that our approach converges to the exact values at high temperature, and agrees well even at moderate-to-low temperatures. We then extend the decimation through the Migdal-Kadanoff procedure to a Hubbard model in d = 3. Phase diagrams are calculated for a range of Coulomb couplings, and two new "" phases are found for hole-dopings of 10 - 18% and 30 - 35%. The electron hopping strength renormalizes to infinity at the T phase sinks, possibly indicating superconductivity, an interpretation further supported by features of the specific heat. The next part turns to the tJ model in d = 3, where the phase was originally observed. In the vicinity of this phase we see a sharp peak in the superfluid weight, and a suppressed low temperature specific heat indicating gap formation. The doping dependence of the free carrier density is similar to that found experimentally in cuprate superconductors. Since strong anisotropy is a key aspect of high-T, materials, we also consider a d = 3 tJ model with distinct in-plane and out-of-plane couplings. We examine the evolution of the phase diagram as the interplane coupling is weakened, and find that the T phase persists even in the quasi-two-dimensional regime.

(cont.) The complex lamellar structure of antiferromagnetic and disordered phases that develops between the T phase and half-filling could be a sign of incommensurate spin ordering. While the pure d = 2 tJ model does not exhibit a phase, we see pre-signatures of it in the renormalization-group flows, and the phase becomes stabilized with a finite transition temperature upon the addition of even the smallest interplane coupling. The last part of the thesis looks at renormalization-group techniques for quenched random systems. As a preliminary step to dealing with disorder in the tJ model, we start with a simpler, yet currently important, classical system, testing a conjecture relating the locations of multicritical points on dual pairs of hierarchical lattice Ising spin glasses. Finally, we incorporate nonmagnetic impurities into the d = 3 tJ model. Small oncentrations of these impurities rapidly destroy the r phase and enhance antiferromagnetism, observations that have parallels in Zn-doped cuprates.