Quantum 2D Heisenberg antiferromagnet: bridging the gap between field-theoretical and semiclassical approaches

TL;DR

This paper bridges the gap between quantum field-theoretical and semiclassical approaches to the 2D Heisenberg antiferromagnet by incorporating non-linear effects and cutoff corrections, leading to consistent correlation length predictions.

Contribution

It introduces a method to include non-linear effects and cutoff corrections, unifying quantum field-theoretical and semiclassical results for the model.

Findings

Cutoff effects induce an effective exchange integral.

The approach accounts for correlation length features at intermediate temperatures.

Quantum and semiclassical results are reconciled.

Abstract

The field-theoretical result for the low-$T$ behaviour of the correlation length of the quantum Heisenberg antiferromagnet on the square lattice was recently improved by Hasenfratz [Eur. Phys. J. B {\bf 13}, 11 (2000)], who corrected for cutoff effects. We show that starting from his expression, and exploiting our knowledge of the classical thermodynamics of the model, it is possible to take into account non-linear effects which are responsible for the main features of the correlation length at intermediate temperature. Moreover, we find that cutoff effects lead to the appearance of an effective exchange integral depending on the very same renormalization coefficients derived in the framework of the semiclassical {\em pure-quantum self-consistent harmonic approximation}: The gap between quantum field-theoretical and semiclassical results is here eventually bridged.