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

Holger Frahm·Alexander R. Its·Vladimir E. Korepin
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Abstract

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 $τ$-function of this system.

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Holger Frahm, Alexander R. Its, Vladimir E. Korepin. 1994-04-28. Differential equation for a correlation function of the spin-${1\over2}$ Heisenberg chain. https://doi.org/10.1016/0550-3213(94)90370-0

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