Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature

TL;DR

This paper investigates the low-temperature behavior of a one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions, revealing how these interactions influence susceptibility, specific heat, and phase transition properties.

Contribution

It introduces a modified spin-wave theory to analyze the model, connecting it with known models and identifying conditions for ordering transitions and estimating critical temperatures.

Findings

Susceptibility and specific heat depend on long-range interaction strength.

The model exhibits an ordering transition for sufficiently long-range interactions.

Critical temperature for phase transition is estimated.

Abstract

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.