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arXiv:cond-mat/0110550 · Journal of the Physical Society of Japan

High Temperature Expansion for the SU(n) Heisenberg Model in One Dimension

Noboru Fukushima, Yoshio Kuramoto

Published May 15, 2002• 10 citations
arXivHTMLPDF

Abstract

Thermodynamic properties of the SU($n$) Heisenberg model in one dimension is studied by means of high-temperature expansion for arbitrary $n$. The specific heat up to $O[(βJ)^{23}]$ and the correlation function up to $O[(βJ)^{18}]$ are derived with $βJ$ being the antiferromagnetic exchange in units of temperature. It is found for $n>2$ that the specific heat shows a shoulder in the high-temperature side of a peak. The origin of this structure is clarified by deriving the temperature dependence of the correlation function. With decreasing temperature, the short-range correlation with two-site periodicity develops first, and then another correlation with $n$-site periodicity at lower temperature. This behavior is in contrast to that of the inverse square interaction model, where the specific heat shows a single peak according to the exact solution. Our algorithm has an advantage that neither computational time nor memory depends on the multiplicity $n$ per site; the series coefficients are obtained as explicit functions of $n$.

DOI
10.1143/jpsj.71.1238

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We discuss the low-temperature specific heat of the integrable SU(N)- invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-mmm tensor representation, especially for the antiferromagnetic coupling. It is known that the linear specific heat coefficient $\gam$ is a function of a field which breaks the SU(N) invariance of the internal degrees of freedom. We calculate the $\gam$ in a zero field and in a small field. The in-field $\gam$ is less than the zero-field $\gam$ as expected since the entropy is reduced in the ordered system. The zero-field $\gam$ is the same as the one obtained by the prediction of the critical behavior of 1D quantum spin systems via conformal field theory. This extends the previous results for N=2 to an arbitrary N.
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