Intermediate-statistics spin waves

TL;DR

This paper introduces a novel intermediate-statistics framework for spin waves (magnons) in Heisenberg systems, providing a new operator realization that naturally incorporates a maximum occupation number, and compares it with existing models and experimental data.

Contribution

It presents an intermediate-statistics representation for magnons that avoids constraints of traditional bosonic models, offering new insights into spin wave behavior and dispersion relations.

Findings

Derived the intermediate-statistics distribution function for magnons.

Calculated dispersion relations for ferromagnetic and antiferromagnetic spin waves.

Compared the spectrum with Bethe ansatz solutions and experimental data.

Abstract

In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein-Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein-Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane-Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest neighbor interaction, and the dipolar interaction into account for comparison with the experiment.