Intermediate temperature dynamics of one-dimensional Heisenberg antiferromagnets

TL;DR

This paper develops a comprehensive theory for the intermediate temperature behavior of one-dimensional Heisenberg antiferromagnets with spin-S ions, providing analytic and numeric results for dynamics and transport properties relevant to experiments.

Contribution

It introduces an effective classical continuum model applicable over a wide temperature range for p-leg ladders, with exact coupling constants and new insights into diffusion in integrable systems.

Findings

Exact results for spin-wave damping

Quantitative predictions for neutron scattering and NMR

Demonstration of diffusion in integrable systems

Abstract

We present a general theory for the intermediate temperature (T) properties of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev, cond-mat/9711014), we argue that an integrable, classical, continuum model of a fixed-length, 3-vector applies over an intermediate temperature range; this range becomes very wide for moderate and large values of 2Sp. The coupling constants of the effective model are known exactly in terms of the energy gap above the ground state (for 2Sp even) or a crossover scale (for 2Sp odd). Analytic and numeric results for dynamic and transport properties are obtained, including some exact results for the spin-wave damping. Numerous quantitative predictions for neutron scattering and NMR experiments are made. A general discussion on the nature of T>0 transport in integrable systems is also presented: an exact solution of a toy model proves that diffusion can exist in integrable systems, provided proper care is taken in approaching the thermodynamic limit.