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arXiv:cond-mat/0509765 · Journal of Statistical Mechanics Theory and Experiment

The finite temperature density matrix and two-point correlations in the antiferromagneticXXZchain

Frank Göhmann, Nils P Hasenclever, Alexander Seel

Published Oct 31, 2005• 18 citations
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Abstract

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length m . On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.

DOI
10.1088/1742-5468/2005/10/p10015

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We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length m . On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.
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We derive a multiple integral representing the ground-state density matrix of a segment of length m of the XXZ spin chain on L lattice sites, which depends on L only parametrically. This allows us to treat chains of arbitrary finite length. Specializing to the isotropic limit of the XXX chain we show for small m that the multiple integrals factorize. We conjecture that this property holds for arbitrary m and suggest an exponential formula for the density matrix which involves only a double Cauchy type integral in the exponent. We demonstrate the efficiency of our formula by computing the next-to-nearest neighbour zz -correlation function for chain lengths ranging from two to macroscopic numbers.