Differential equation for a correlation function of the spin-12 Heisenberg chain
Holger Frahm, Alexander R. Its, Vladimir E. Korepin
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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