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

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

2006-03-08

arxiv.org/abs/hep-th/0603064v3

J.Stat.Mech.0604:P04001,2006

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, v2: a paragraph in the introduction rewritten, v3: typo in eqn. (29) corrected, a few words changed

Scientific paper

10.1088/1742-5468/2006/04/P04001

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' $\xi_j$. 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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