Differential equation for a correlation function of the spin-$\frac{1}{2}$ Heisenberg chain

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 $\tau$-function of this system.

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

References in corpus (2)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Correlation Function of the Spin-1/2 XXX Antiferromagnet

Cited by in corpus (2)

• Integro-Difference Equation for a correlation function of the spin-$\frac{1}{2}$ Heisenberg XXZ chain
• Operator-valued Riemann-Hilbert problem for correlation functions of the XXZ spin chain