The overarching goal of my research is the theoretical and computational study of strongly correlated electron systems, and the understanding of the complexity that emerges from these systems at the nanoscale. Within this theme, my research comprises classical systems, spin-fermion models and fully quantum mechanical models.
Part of my research has focused on the study of spin-fermion models for manganites, and the understanding of the colossal magneto-resistive (CMR) effect. We have found that the CMR is associated with short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge ordered arrangement that appears at low-temperature. These polarons appear in states with nanoscale inhomogeneities that emerge from the competing interactions in the system.
The emerging nanoscale complexity found in manganites is found in other strongly correlated electron systems as well. I have used spin-fermion models to study the pseudo-gap phase of cuprate high temperature superconductors. We have developed a comprehensive theory of the pseudo-gap phase based on the competition between antiferromagnetism and superconductivity. We have extracted the local density of states measurements from this model and compared them with Scanning tunneling microscope (STM) measurements. We have also recently studied the Fermi surface obtained from our theory, and compared it with angle- resolved photo-emission spectroscopy measurements for cuprates. We have found that a state with nano-scale antiferromagnetic and superconducting clusters is in agreement with both STM and ARPES measurements.
Finally, for fully quantum systems, I have developed DMRG++, an implemen- tation of the DMRG algorithm that emphasizes generic programming using C++ templates. DMRG++ and our equivalent code for quantum Monte Carlo simula simulations, DCA++, is part of our effort to create computational kernels or solvers for condensed-matter models, such as the Hubbard model.