2002/12/05 by Noboru Fukushima, Fukushima, Noboru
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0212123
20 pages, 30 figures, to appear in J. Stat. Phys
arxiv created 2002/12/05 · arxiv updated 2009/11/30
We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU(n) Heisenberg model with arbitrary n. The new method is a novel extension of the well-established finite cluster method. Our method emphasizes hidden combinatorial aspects of the high-temperature series expansion, and solves the long-standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites. Series coefficients are expressed in terms of cumulants, which are shown to have the property that all deviations from the lowest-order nonzero cumulant can be expressed in terms of a particular kind of moment expansion. These ``quasi-moments'' can be written in terms of corresponding ``quasi-cumulants'', which enable us to calculate higher-order terms in the high-temperature series expansion. We also present a new technique for obtaining the low-order contributions to specific heat from finite clusters.