A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas

TL;DR

This paper establishes a continuum limit connecting the spin-1/2 XXZ chain to the 1D Bose gas, enabling the derivation of Bose gas correlation functions at various temperatures from the spin chain data.

Contribution

It introduces a novel continuum limit relating the spin chain to the Bose gas and derives correlation functions at arbitrary temperatures using the quantum transfer matrix approach.

Findings

Derived a continuum limit linking the spin chain and Bose gas.

Obtained expressions for Bose gas correlation functions at arbitrary temperatures.

Connected scattering data of the spin chain to the properties of the Bose gas.

Abstract

By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.