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
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.
PACS: 75.10.Jm – Quantized spin models / 75.50.Ee – Antiferromagnetics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998