Eur. Phys. J. B 2, 501-507 (1998)
https://doi.org/10.1007/s100510050274

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

¹ Institut für Theoretische Physik, Universität Hannover, 30167 Hannover, Germany
² Laboratoire de Physique Théorique des Liquides, Université P. et M. Curie, case 121, 4 Place Jussieu, 75252 Paris Cedex 05, France
³ Groupe de Physique Statistique, Université de Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, France
⁴ Université Paris-X, 92001 Nanterre Cedex, France

Corresponding author: ^a waldtman@itp.uni-hannover.de

Received: 27 November 1997
Accepted: 29 January 1998
Published online: 15 April 1998

Abstract

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets.