High Temperature Expansion for Frustrated and Unfrustrated S=12 Spin Chains.pdfVIP

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High Temperature Expansion for Frustrated and Unfrustrated S=12 Spin Chains.pdf

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High Temperature Expansion for Frustrated and Unfrustrated S=12 Spin Chains

a r X i v : c o n d - m a t / 0 0 0 3 2 2 1 v 2 [ c o n d - m a t .s t r - e l ] 7 A p r 2 0 0 0 High Temperature Expansion for Frustrated and Unfrustrated S= 1 2 Spin Chains Alexander Bu?hler1? Norbert Elstner2? and Go?tz S. Uhrig1? 1 Institut fu?r Theoretische Physik, Universita?t zu Ko?ln, Zu?lpicher Str. 77, D-50937 Ko?ln, Germany 2 Physikalisches Institut, Universita?t Bonn, Nu?allee 12, D-53115 Bonn, Germany (1st February 2008) A computer aided high temperature expansion of the mag- netic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations are performed in the integer domain. They are provided in the form of polynomials allowing quick and easy fits. Various representations of the results are discussed. Combining high temperature expansion coefficients and dispersion data yields very good agreement already in low order of the expansion which makes this approach very promising for the application to other problems, for instance in higher dimensions. 05.10.-a, 75.40.Cx, 75.10.Jm, 75.50.Ee I. INTRODUCTION Spin systems are among the most investigated systems in solid state physics. They represent problems with high correlation since the spin algebra does not have the sim- plicity of the fermionic or the bosonic algebra. This can also be seen from the generic derivation of antiferromag- netic spin models from a half-filled Hubbard model in the limit of large interactionU → ∞. Hence even the calcula- tion of simple properties like the magnetic susceptibility χ or the magnetic specific heat C is not straightforward. Experimentally, however, susceptibility and specific heat are the first quantities used to characterise a compound. So quantitative theoretical predictions are very impor- tant to pinpoint the appropriate model. Quantum Monte Carlo methods underwent consider- able progress in the last years so that the calculation of χ and