Research Objectives
To study strongly correlated electron effects in various Hubbard models using the constrained-path Monte Carlo method.
Computational Approach
We are using a parallelized version of the constrained-path Monte Carlo method recently proposed by Zhang, Carlson, and Gubernatis. This method projects the ground-state wavefunction from a trial wavefunction by a branched random walk, and eliminates the infamous fermion sign problem by eliminating any random walker that develops a negative overlap with a constraining wavefunction. If this constraining wavefunction were the exact ground-state wavefunction, the procedure would be exact. Because only an approximate ground state can be used, a variational upper bound to the exact ground-state energy is produced. Benchmarking has demonstrated that this bound is tight and that the Monte Carlo representation of the wavefunction produces good approximations to other physical quantities like pairing correlation functions.
Accomplishments
We focused on simulations of the two-dimensional, three-band Hubbard model, one of the three most studied possible models of high temperature superconducting materials. We completed a series of computations of the hole binding energy and the superconducting pairing correlations functions. We found that over a wide range of physically relevant parameters two doped holes bind, but the pairing correlation functions decay rapidly with distance. In particular, these correlations decay much more rapidly for extended s-wave correlations than they do for d-wave correlations. Furthermore, increasing the strength of the copper-site Coulomb repulsion suppressed the longer-ranged pairing correlations. These longer-ranged correlations are also suppressed with increasing system size.
Presently we are developing extensions of the constrained-path Monte Carlo method that will permit the use of a greater variety of constraining wavefunctions, such as the fixed-particle number BCS and the spin-density-wave wavefunctions. We are also considering a study of the effects of a dimerized lattice on hole binding.
Significance
We do not find evidence of off-diagonal long-range superconducting order. Because of the variational nature of our computational method, our results do not prove that the three-band Hubbard model, the most studied model of high temperature superconductivity, does not superconduct. However, our results, plus previous similar null results on the one-band Hubbard model, darken hopes that these models will serve as useful paradigms for the superconducting phase of high temperature superconducting materials.
The reported activity is a sub-project of a broader project applying a variety of computational methods to various models of strongly interacting electrons in novel materials in reduced dimensions.
Publications
1. Shiwei Zhang, J. Carlson, and J. E. Gubernatis, "Constrained path Monte Carlo method for fermion ground states," Phys. Rev. B 55, 7464 (1997).
2. Shiwei Zhang, J. Carlson, and J. E. Gubernatis, "Pairing correlations in the two-dimensional Hubbard model," Phys. Rev. Lett. 78, 4486 (1997).
3. M. Guerrero, J. E. Gubernatis, and Shiwei Zhang, "Quantum Monte Carlo study of pairing correlations in the three-band Hubbard model," Phys. Rev. B, submitted.
URL
http://bifrost.lanl.gov/~jeg/jeg.html
Distance dependence of the vertex contribution to the d-wave pairing correlation function
for different values of the copper-site Coulomb repulsion.