Nonlinear sigma Model Treatment of Quantum Antiferromagnets in a Magnetic Field

TL;DR

This paper uses a nonlinear sigma model to analyze low-dimensional quantum antiferromagnets in magnetic fields, predicting magnetization and correlation functions, and aligning well with experimental data.

Contribution

It introduces a comprehensive theoretical framework combining spin stiffness, 1/N expansion, and renormalization group methods for quantum antiferromagnets in magnetic fields.

Findings

Predicted magnetization and critical fields match experimental data.

Described quantum fluctuations restoring symmetry at low fields.

Provided detailed spin correlation functions and decay exponents.

Abstract

We present a theoretical analysis of the properties of low-dimensional quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model description, we use a spin stiffness analysis, a 1/N expansion, and a renormalization group approach to describe the broken-symmetry regimes of finite magnetization, and, in cases of most interest, a low-field regime where symmetry is restored by quantum fluctuations. We compute the magnetization, critical fields, spin correlation functions, and decay exponents accessible by nuclear magnetic resonance experiments. The model is relevant to many systems exhibiting Haldane physics, and provides good agreement with data for the two-chain spin ladder compound CuHpCl.