Rachel Wortis

Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems

We test the usefulness of a generalized inverse participation ratio (GIPR) as a measure of Anderson localization. The GIPR differs from the usual inverse participation ratio in that it depends on the local density of states rather than on the single-electron wavefunctions. This makes it suitable for application to many-body systems. We benchmark the GIPR by performing a finite-size scaling analysis of a disordered, noninteracting, three-dimensional tight-binding lattice. We find values for the critical disorder and critical exponents that are in agreement with published values.

Dynamical mean field study of the two-dimensional disordered Hubbard model

We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Greens function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.

Renormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite Temperature

We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at nonzero temperature. We begin by introducing the scaling ansatz for purely one-dimensional fermion systems and its extension when interchain coupling and dimensionality crossovers are present at finite temperature. Next, we review the application of the renormalization group technique to the one-dimensional electron gas model and clarify some peculiarities of the method at the two-loop level. The influence of interchain coupling is then included and results for the crossover phenomenology and the multiplicity of characteristic energy scales are summarized. The emergence of the Kohn-Luttinger mechanism in quasi-one-dimensional electronic structures is discussed for both superconducting and density-wave channels.

Geometrically averaged density of states as a measure of localization

Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states,

Local integrals of motion in the two-site Anderson-Hubbard model

\rho_g(\omega)

Temperature dependence of the zero-bias anomaly in the Anderson?Hubbard model: insights from an ensemble of two-site systems

, as an order parameter for the Anderson transition is examined. In the context of finite-size systems we examine complications which arise from finite energy resolution. Furthermore we demonstrate that even in infinite systems a decline in

Effects of strong correlations on the disorder-induced zero-bias anomaly in the extended Anderson-Hubbard model

\rho_g(\omega)

Calculated NMR T 2 relaxation due to vortex vibrations in cuprate superconductors

with increasing disorder strength is not uniquely associated with localization.

Nonlocal conductivity in the vortex-liquid regime of a two-dimensional superconductor.

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins in specific systems is non-trivial. Given continuing intense interest in the role of disorder in strongly correlated systems, we consider the disordered Hubbard model. By studying a small system we provide concrete examples of the form of local integrals of motion in the Anderson-Hubbard model. Moreover, we are able not only to identify the most local choice but also to explore the nature of the distribution of possible choices. We track the evolution of the optimally localized pseudospins as hopping and interactions are varied to move the system away from the trivially localized atomic limit.

Disorder-induced zero-bias anomaly in the Anderson-Hubbard model: Numerical and analytical calculations

Motivated by experiments on doped transition metal oxides, this paper considers the interplay of interactions, disorder, kinetic energy and temperature in a simple system. An ensemble of two-site Anderson-Hubbard model systems has already been shown to display a zero-bias anomaly (Wortis and Atkinson 2010 Phys. Rev. B 82 073107) which shares features with that found in the two-dimensional Anderson-Hubbard model (Chiesa et al 2008 Phys. Rev. Lett. 101 086401). Here the temperature dependence of the density of states of this ensemble is examined. In the atomic limit, there is no zero-bias anomaly at zero temperature, but one develops at small nonzero temperatures. With hopping, small temperatures augment the zero-temperature kinetic-energy-driven zero-bias anomaly, while at larger temperatures the anomaly is filled in.