Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field

TL;DR

This paper derives compact formulas for spin-spin correlation functions in the XXZ Heisenberg chain under a magnetic field using algebraic Bethe ansatz, providing explicit integral representations for different lattice distances.

Contribution

It introduces a new compact formula for the multiple action of transfer matrix operators, enabling explicit computation of correlation functions in the thermodynamic limit.

Findings

Correlation functions expressed as sums of m multiple integrals

Integral representations depend on lattice distance as a power of a simple function

Derived compact formulas facilitate calculations for arbitrary spectral parameters

Abstract

Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At lattice distance m, they are typically given as the sum of m terms. Each term n of this sum, n = 1,...,m is represented in the thermodynamic limit as a multiple integral of order 2n+1; the integrand depends on the distance as the power m of some simple function. The root of these results is the derivation of a compact formula for the multiple action on a general quantum state of the chain of transfer matrix operators for arbitrary values of their spectral parameters.