Universal temperature dependence of the magnetization of gapped spin chains

TL;DR

This paper demonstrates that the temperature at which magnetization reaches a minimum in gapped spin chains is a universal feature, supported by quantum Monte Carlo simulations and Tomonaga-Luttinger liquid theory, useful for estimating energy gaps.

Contribution

The study reveals the universal nature of the magnetization minimum in gapped spin chains and connects it with theoretical predictions and numerical data.

Findings

Magnetization exhibits a universal minimum at finite temperature.

Quantum Monte Carlo confirms the minimum in the gapless regime.

The minimum can be used to estimate the energy gap from experimental data.

Abstract

Temperature dependence of the magnetization of the Haldane spin chain at finite magnetic field is analyzed systematically. Quantum Monte Carlo data indicates a clear minimum of magnetization as a function of temperature in the gapless regime. On the basis of the Tomonaga-Luttinger liquid theory, we argue that this minimum is rather universal and can be observed for general axially symmetric quasi-one-dimensional spin systems. Our argument is confirmed by the magnetic-field dependence of the spin-wave velocity obtained numerically. One can estimate a magnitude of the gap of any such systems by fitting the experimental data with the magnetization minimum.