Luttinger liquid parameter for the spin-1 Heisenberg chain in a magnetic field

TL;DR

This paper combines a new formula and previous numerical data to analyze how the transverse correlation exponent in a spin-1 Heisenberg chain varies with magnetization under a magnetic field, comparing it with theoretical models.

Contribution

It provides a derived formula for the transverse correlation exponent in the spin-1 Heisenberg chain in a magnetic field, linking numerical results with theoretical predictions.

Findings

Transverse correlation exponent eta varies as 1/2 - 2.0*m + O(m^2) with magnetization m.

Comparison with the O(3) non-linear sigma-model supports the derived behavior.

The study bridges numerical results and theoretical models for the spin-1 chain in a magnetic field.

Abstract

A recently derived general formula and older numerical results are combined to deduce the behavior of the transverse correlation exponent for the spin-1 Heisenberg antiferromagnetic chain in an applied magnetic field: eta = 1/2 - (2.0)m +O(m^2), where m is the magnetization per site. A comparison with the O(3) non-linear sigma-model is also made.