Many of the properties of solids can be well explained with approximate treatment of interactions between the electrons. However, other properties, notably magnetism, require more rigorous treatment of correlations. QMC is a technique which allows one to study such interacting electron systems exactly, at least to within statistical sampling errors and finite size limitations.

The Hubbard Hamiltonian is a simple tight binding model of interacting electrons which for the last three decades has been the central paradigm in attempts to understand basic theoretical issues like metal-insulator transitions and magnetism in solids. Interest in it has been greatly heightened by the possibility that it holds the key to explaining the vanishing of resistance in high temperature superconductors.

The ground state of the Hubbard model in two dimensions, at half-filling, is known to have long range antiferromagnetic order, and also to be insulating. Using QMC, we explored a number of fundamental theoretical issues related to what happens to magnetic and charge correlations when different types of disorder are introduced. There are fascinating experimental implications, including the possibility of a universal resistance at the superconducting-insulating phase boundary in thin films, the metal-insulator transition in doped semiconductors and the effect of non-magnetic impurities in high temperature superconductors, which we were able to address. We have been the first group to conduct extensive path integral QMC simulations of 2D Hubbard models with disorder.

Relevant Publications:

[63.] N. Trivedi, R.T. Scalettar, and M. Randeria, ``Superconductor-Insulator Transition in a Disordered Electronic System,'' Phys. Rev. B54, 3756 (1996).
[67.] C. Huscroft and R.T. Scalettar, ``Effect of Disorder on Charge Density Wave and Superconducting Order in the Half-Filled Attractive Hubbard Model,'' Phys. Rev. B55, 1185 (1997).
[70.] M. Ulmke and R.T. Scalettar, ``Magnetic Correlations in the Two Dimensional Anderson-Hubbard Model,'' Phys. Rev. B55, 4149 (1997).
[76.] M. Ulmke, P.J.H. Denteneer, R.T. Scalettar, G.T. Zimanyi, ``Enhancement of Long Range Antiferromagnetic Order by Nonmagnetic Impurities in the Hubbard Model,'' Europhys. Lett. 42, 655 (1998).
[77.] P.J.H. Denteneer, M. Ulmke, R.T. Scalettar, G.T. Zimanyi, ``Ordered States in the Disordered Hubbard Model,'' Physica A251, 162 (1998).
[80.] C. Huscroft and R.T. Scalettar, ``Evolution of the Density of States Gap in a Disordered Superconductor,'' Phys. Rev. Lett. 81, 2775 (1998).
[92.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, "Conducting phase in the two-dimensional disordered Hubbard model", Phys. Rev. Lett. 83, 4610 (1999).
[108.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, ``Particle-Hole Symmetry and the Effect of Disorder on the Mott--Hubbard Insulator,'' Phys. Rev. Lett. 87, 6401 (2001).
[125.] P.J.H. Denteneer and R.T. Scalettar, "Interacting electrons in a two-dimensional 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," Pramana-J. 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).
[163.] N. Paris, A. Baldwin, and R.T. Scalettar, "Mott and Band Insulator Transitions in the Binary Alloy Hubbard Model," Phys. Rev. B75, 165113 (2007).
[166.] P.B. Chakraborty, P.J.H. Denteneer, and R.T. Scalettar, "Determinant quantum Monte Carlo study of the screening of the one-body potential near a metal-insulator transition," Phys. Rev. B75, 125117 (2007).
[173.] K. Aryanpour, T. Paiva, W.E. Pickett, and R.T. Scalettar, "Effect of Inhomogeneity on s-wave Superconductivity in the Attractive Hubbard Model," Phys. Rev. B76, 184521 (2007).
[179.] G.G. Batrouni, H.R. Krishnamurthy, K.W. Mahmud, V.G. Rousseau, and R.T. Scalettar, "Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap," Phys. Rev. A78 023627 (2008).
[181.] Simone Chiesa, Prabuddha B. Chakraborty, Warren E. Pickett, and Richard T. Scalettar, "Disorder-induced stabilization of the pseudogap in strongly correlated systems," Phys. Rev. Lett. 101, 086401 (2008).
[182.] F. Mondaini, T. Paiva, R.R. dos Santos, and R.T. Scalettar, "Disordered Superconductors: roles of temperature and interaction strength," Phys. Rev. B78, 174519 (2008).
[185.] Marcos Rigol, George G. Batrouni, Valery G.~Rousseau, and Richard T. Scalettar, "Universal state diagrams for harmonically trapped bosons in optical lattices," Phys. Rev. A79, 053605 (2009).