First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagom\'e lattice

TL;DR

This paper investigates the low energy spectra of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice, revealing a unique spin liquid state with unusual excitations and potential chiral order, distinct from known spin liquids.

Contribution

It provides exact low energy spectra for small kagomé lattice samples, showing the system's distinct spin liquid properties and possible chiral order, advancing understanding of frustrated quantum antiferromagnets.

Findings

Ground state is a spin liquid with a gap to magnetic excitations.

Nonmagnetic excitations form a gapless continuum in the thermodynamic limit.

Samples with odd sites show symmetries supporting potential chiral order.

Abstract

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagom\'e 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 N\'eel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic ($\Delta S=1$) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic ($\Delta S=0$) 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 kagom\'e 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.