Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{\'e} lattice: an approach through exact spectra analysis

TL;DR

This study analyzes the low-energy spectra of small kagome lattice antiferromagnets to understand quantum fluctuations and challenges the 'order by disorder' hypothesis, revealing a quantum critical point influenced by second neighbor interactions.

Contribution

It provides a symmetry-based spectral analysis of small samples, offering new insights into quantum fluctuations and phase stability in the kagome Heisenberg antiferromagnet.

Findings

Contradicts the 'order by disorder' scenario from large S calculations.

Identifies a quantum critical point at non-zero second neighbor coupling.

Shows the necessity of ferromagnetic second neighbor exchange to stabilize certain patterns.

Abstract

A group symmetry analysis of the low lying levels of the spin-1/2 kagom\'e Heisenberg antiferromagnet is performed for small samples up to N=27. This approach allows to follow the effect of quantum fluctuations when the sample size increases. The results contradict the scenario of ``order by disorder'' which has been advanced on the basis of large S calculations. A large enough second neighbor ferromagnetic exchange coupling is needed to stabilize the $\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantum critical transition at a non zero coupling.