We analyzed the localization transition
of hardcore bosons with random site energies
in mean field theory. It had often been asserted that no such
transition could occur, because the perfect connectivity of the mean
field lattice enabled particles to move between
sites with similar energies without passing through intermediate
states which were not in resonance. We showed that this statement was
not true, and that with an appropriate choice of site energy
distribution a localization transition can occur.
We characterized this transition using
the inverse participation ratio, the single site Green's function,
the superfluid order parameter and the
corresponding susceptibility, determining the appropriate
exponents.
We developed
a theory for the quantum gauge glass, by considering disorder in both
the off diagonal (hopping) terms and the site energies.
This model is closely related to XY magnets and bosons in random media.
Materials which are realizations of such spinglass models include the
LiHoYF compounds. A crucial unresolved issue has been to
explain the behavior of the nonlinear susceptibility
which does not diverge experimentally, but was found to diverge in
recent theoretical studies. We calculated the phase diagram which
consists of a superfluid phase, and Weak and Strong Glass regions.
Strikingly, at the
Strong Glass transition the nonlinear susceptibility does not diverge.
We have also revisited an old problem concerning the relation between
critical exponents in disordered classical systems.
We showed that the often quoted ``Chayes inequality'' is, in
fact, generated only by the procedure used to do the disorder
averaging, and different procedures give quite different
exponent bounds. This work attracted considerable interest
as it challenged a commonly held truth in critical phenomena.
We also introduced a new procedure to analyze the shifts in critical
points on finite lattices.
Finally, the study of disordered Hubbard models and the possibility of
a twodimensional metalinsulator transition has been of interest to us.
We showed that the onsite U in the Hubbard Hamiltonian
can change the qualitative temperature dependence of the conductivity
from insulating to metallic.
Relevant Publications:
[61.]
F. Pazmandi, G.T. Zimanyi and R.T. Scalettar,
``Meanfield Theory of the Localization Transition,''
Phys. Rev. Lett. 75, 1356 (1995).


[65.]
F. Pazmandi, G.T. Zimanyi and R.T. Scalettar,
``MeanField Theory for Quantum Gauge Glasses,''
Europhys. Lett. 38, 255 (1997).


[79.]
F. Pazmandi, R.T. Scalettar and G.T. Zimanyi,
``Revisiting the Theory of Finite Size Scaling in Disordered
Systems: nu Can Be Less Than 2/d,''
Phys. Rev. Lett. 79, 5130 (1997).


[80.]
C. Huscroft and R.T. Scalettar,
``Evolution of the Density of States Gap in
a Disordered Superconductor",
Phys. Rev. Lett. 81, 2775 (1998).


[84.]
M. Ulmke, P. J. H. Denteneer, V. Janis, R. T. Scalettar, A. Singh,
D. Vollhardt, and G. T. Zimanyi,
``Disorder and Impurities in Hubbard Antiferromagnets",
Advances in Solid State Physics, 38, 369 (1999).


[86.]
R.T. Scalettar, N. Trivedi, C. Huscroft, and M. Randeria,
``Quantum Monte Carlo Study of the Disordered, Attractive Hubbard Model",
Phys. Rev. B59, 4364 (1999).


[92.]
P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi,
``Conducting phase in the
twodimensional disordered Hubbard model",
Phys. Rev. Lett. 83, 4610 (1999).


[108.]
P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi,
``ParticleHole Symmetry and the
Effect of Disorder on the MottHubbard Insulator,''
Phys. Rev. Lett. 87, 6401 (2001).


[125.]
P.J.H. Denteneer and R.T. Scalettar,
"Interacting electrons in a twodimensional disordered environment:
Effect of a Zeeman magnetic field,''
Phys. Rev. Lett. 90, 246401 (2003).


[138.]
N. Trivedi, P.J.H. Denteneer, D. Heidarian, and R.T. Scalettar,
"Effect of Interactions, Disorder and Magnetic Field in the 2D Hubbard
Model,''
PramanaJ. of Physics 64, 1051 (2005).

[147.]
Daniel Hurt, Evan Odabashian, Warren Pickett, Richard Scalettar,
Felipe Mondaini, Thereza Paiva, and Raimundo dos Santos,
"Destruction of Superconductivity by Impurities
in the Attractive Hubbard Model",
Phys. Rev. B72, 144513 (2005).


[148.]
K. Aryanpour, R.T. Scalettar, W.E. Pickett, T.C. de Lacerda Paiva,
M. Mayr, and E. Dagotto,
"Effect of Inhomogeneity on swave Superconductivity in the
Attractive Hubbard Model",
Phys. Rev. B73, 104518 (2006).


[151.]
C.M. Chaves, T. Paiva, J. d'Albuquerque e Castro, F. Hebert,
R.T. Scalettar, G.G. Batrouni, and B. Koiller,
"The magnetic susceptibility of exchangedisordered
antiferromagnetic finite chains",
Phys. Rev. B73, 104410 (2006).

