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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
; | | Date: |
8 Mar 2006 | | Subject: | High Energy Physics - Theory; Statistical Mechanics | | 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’ $xi_j$. 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. | | Source: | arXiv, hep-th/0603064 | | Services: | Forum | Review | PDF | Favorites | |
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