Density matrices for finite segments of Heisenberg chains of arbitrary length

Details Density matrices for finite segments of Heisenberg chains of arbitrary length Density matrices for finite segments of Heisenberg chains of arbitrary length

2007-01-18

arxiv.org/abs/cond-mat/0701463v3

J. Phys. A 40 (2007) 4439-4453

Physics

Condensed Matter

Statistical Mechanics

19 pages, Latex, 3 figures; v2 minor corrections, a reference updated, v3 typos in the text and in eq. (54) corrected

Scientific paper

10.1088/1751-8113/40/17/002

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.

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