Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields

Details Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields

2003-08-14

arxiv.org/abs/cond-mat/0308298v1

J. Phys. Soc. Jpn. 73, 1482 (2004)

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages with 4 figs

Scientific paper

10.1143/JPSJ.73.1482

An improved algorithm is proposed for Monte Carlo methods to study fermion systems interacting with adiabatical fields. To obtain a weight for each Monte Carlo sample with a fixed configuration of adiabatical fields, a series expansion using Chebyshev polynomials is applied. By introducing truncations of matrix operations in a systematic and controlled way, it is shown that the cpu time is reduced from O(N^3) to O(N) where N is the system size. Benchmark results show that the implementation of the algorithm makes it possible to perform systematic investigations of critical phenomena using system-size scalings even for an electronic model in three dimensions, within a realistic cpu timescale.

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