Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apr.i7002z&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
Quantum Monte Carlo methods are widely applied to study many-fermion systems. In condensed matter physics, methods utilizing the auxiliary-field formalism, which are closely related to their counterparts in nuclear and high-energy physics, have been used extensively to study important basic models. We describe recent developments in dealing with the fermion sign problem in these methods. The Monte Carlo process is formulated as branching random walks in a space of Slater determinants. A boundary condition is derived for the random walks which eliminates any negative sign in the Monte Carlo samples. Both ground-state(Shiwei Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. B 55), 7464 (1997). and finite-temperature(Shiwei Zhang, Phys. Rev. Lett. 83), 2777 (1999). methods have been developed. They allow simulations of many-fermion systems at large system sizes and low temperatures. The new methods, which are approximate, yield accurate results in benchmark calculations. We show applications of these methods to calculate properties of the Hubbard model, which has played a central role in the intense theoretical effort to understand high-temperature superconductivity. We then discuss auxiliary-field methods for more realistic electronic systems, where the more general form of interactions can lead to complex auxiliary fields. The sign problem now becomes a phase problem. We present an approximate method we have recently developed(Shiwei Zhang and H. Krakauer, preprint.) to control this problem.
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