Differential equation for a correlation function of the spin-${1\over2}$ Heisenberg chain

Details Differential equation for a correlation function of the spin-${1\over2}$ Heisenberg chain Differential equation for a correlation function of the spin-${1\over2}$ Heisenberg chain

1994-04-28

arxiv.org/abs/cond-mat/9404091v1

Nucl. Phys. B428 FS (1994) 694

Physics

Condensed Matter

18 pp, LaTeX, ITP-UH-06/94, ITP-SB-94-16

Scientific paper

10.1016/0550-3213(94)90370-0

We consider the probability to find a string of $x$ adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation funtion is a $\tau$-function of this system.

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