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Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain

Herman E. Boos·Frank Göhmann·Andreas Klümper·Junji Suzuki
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Abstract

We consider the inhomogeneous generalization of the density matrix of a finite segment of length $m$ of the antiferromagnetic Heisenberg chain. It is a function of the temperature $T$ and the external magnetic field $h$, and further depends on $m$ `spectral parameters' $ξ_j$. For short segments of length 2 and 3 we decompose the known multiple integrals for the elements of the density matrix into finite sums over products of single integrals. This provides new numerically efficient expressions for the two-point functions of the infinite Heisenberg chain at short distances. It further leads us to conjecture an exponential formula for the density matrix involving only a double Cauchy-type integral in the exponent. We expect this formula to hold for arbitrary $m$ and $T$ but zero magnetic field.

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Herman E. Boos, Frank Göhmann, Andreas Klümper, Junji Suzuki. 2006-04-07. Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain. https://doi.org/10.1088/1742-5468%2F2006%2F04%2Fp04001

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