QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime

TL;DR

This paper presents an integral solution to the qKZ equation with |q|=1 and proposes a conjectural formula for XXZ model correlation functions in the gapless regime, verified in special cases including XXX and XY limits.

Contribution

It introduces a new integral solution to the qKZ equation at |q|=1 and formulates a conjecture for the XXZ correlation functions in the gapless phase.

Findings

Integral solution to qKZ with |q|=1 provided.

Conjectural formula for XXZ correlation functions proposed.

Verification in special cases including XXX and XY limits.

Abstract

An integral solution to the quantum Knizhnik-Zamolodchikov ($q$KZ) equation with $|q|=1$ is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest neighbor correlator with an arbitrary coupling constant, and general correlators in the XXX and XY limits.