Three-Dimensional Ordering in Weakly Coupled Antiferromagnetic Ladders and Chains

TL;DR

This paper develops a theoretical framework for understanding magnetic-field induced three-dimensional ordering in weakly coupled antiferromagnetic chains and ladders, revealing a Bose condensate nature of the ordered phase.

Contribution

It introduces a comprehensive method combining effective field theories, Bethe ansatz, and RPA to analyze 3D ordering in anisotropic quantum antiferromagnets, including higher-spin systems.

Findings

Derived effective continuum field theories for 1D subsystems.

Calculated Luttinger parameters using Bethe ansatz.

Identified the 3D ordering transition line with RPA.

Abstract

A theoretical description is presented for low-temperature magnetic-field induced three-dimensional (3D) ordering transitions in strongly anisotropic quantum antiferromagnets, consisting of weakly coupled antiferromagnetic spin-1/2 chains and ladders. First, effective continuum field theories are derived for the one-dimensional subsystems. Then the Luttinger parameters, which determine the low-temperature susceptibilities of the chains and ladders, are calculated from the Bethe ansatz solution for these effective models. The 3D ordering transition line is obtained using a random phase approximation for the weak inter-chain (inter-ladder) coupling. Finally, considering a Ginzburg criterion, the fluctuation corrections to this approach are shown to be small. The nature of the 3D ordered phase resembles a Bose condensate of integer-spin magnons. It is proposed that for systems with higher spin degrees of freedom, e.g. N-leg spin-1/2 ladders, multi-component condensates can occur at high magnetic fields.