James Gubernatis, Joseph Carlson, Mariana Guerrero, and
Gerardo Ortiz, Los Alamos National Laboratory
Janez Bonca, Institut Jozef Stefan, Slovenia

Research Objectives

Our objective is to apply novel numerical methods to determine the properties of strongly interacting electron systems in reduced (mainly two) dimensions. A prototypical problem that we are considering is to identify a possible microscopic model for high temperature superconductivity.

Computational Approach

We developed the constrained path Monte Carlo (CPMC) method as a way to eliminate the "sign problem" that plagues many Monte Carlo simulations of fermion systems. In the CPMC method, the overlap of the wave function is constrained by a trial function, which prevents the probability associated with the Monte Carlo sampling from becoming negative. However, even with an approximate trial function, CPMC results for the two-dimensional Hubbard model compare quite well with exact diagonalization results, with much less computer time required than with other fermion quantum Monte Carlo (QMC) methods. Another advantage of CPMC over other methods is that it allows us to study larger system sizes, which is important for eliminating finite size effects that could bias the computed results.

Accomplishments

We made several important improvements to our original version of CPMC. One was extending the method to use generalized Hartree-Fock wave functions as the initial, guiding, and constraining states. This allowed us to illustrate the remarkable lack of bias these states impose on the final solution. Another extension was to systems of electrons in strong magnetic fields. Here, instead of a sign problem, the simulations are faced with a phase problem, as Monte Carlo sampling from complex-valued distribution functions is required.

Our continued use of CPMC is focused on expanding the range of models and physical systems studied with it. We are in the midst of extensive simulations of the two-dimensional periodic Anderson Model, finding what we believe is an electron doping range where the ground state is one of partially saturated ferromagnetic. This range differs from that predicted by such commonly used approximators as dynamical mean field theory and the slave boson method. We just completed a series of simulations of the attractive Hubbard model, which is a system with no sign problem. Having now an exact method, we compared the results of the simulations with the predictions of the BCS approximation to determine empirically its range of fidelity. One result is illustrated in the accompanying figure.

The QMC and BCS on-site s-wave pairing correlation function as a function of the distance R between pairs for an 8 × 8, quarter-filled, attractive Hubbard model at U/t = 1, 2, and 4. U/t parameterizes the interaction strength.

Significance

Reduced-dimensional systems typically exhibit a richness of novel phases which are accompanied by unusual magnetic and electrical properties. These phases and their properties present challenges to our understanding, but also present important opportunities for improving energy transmission and storage, optical switches and displays, computer memories and chips, etc. The identification of experimental probes that signal the appearance of such novel effects is an important goal of this project.

Publications

J. Bonca and J. E. Gubernatis, "Effects of doping on spin correlations in the periodic Anderson model," Phys. Rev. B 58, 6992 (1998).

M. Guerrero, G. Ortiz, and J. E. Gubernatis, "Correlated wave functions and the absence of long-range order in numerical studies of the Hubbard model," Phys. Rev. B 59, 1706 (1999).

J. Carlson, G. Ortiz, J. E. Gubernatis, and Shiwei Zhang, "Some issues and observations about the constrained path Monte Carlo method," Phys. Rev. B 59, 12788 (1999).

http://bifrost.lanl.gov/~jeg/jeg.html