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

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 (∆S = 1) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic (∆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 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.

RVB description of the low-energy singlets of the spin 1/2 kagomé antiferromagnet

“…Moreover, the shape of the spectrum is very similar to the one obtained by exact diagonalization (ED) [2]. In order to test this point more precisely, we have again computed α(∆) at the isotropic point (see Fig.…”

“…Since the particular low-temperature dependence of many physical quantities is directly connected to the structure of this non-magnetic part of the spectrum, many recent works [2,5,6,7,8,9,10,11] were devoted to understand the nature of the disordered GS and low-lying excitations. Unfortunately, it is still hard to come up with a clear picture of the low-energy sector of the KAF.…”

Accurate results from perturbation theory for strongly frustratedS=12Heisenberg spin clusters

“…The apparent singlet nature of the excitation spectrum in the Kagomé lattice arises from frustration [18,26] and leads to a large non magnetic contribution to the entropy of the system at low temperatures. This is an important feature in analysis of experimental data on any physical realization of a Kagomé lattice.…”

Quantum Phases in Two-Dimensional Frustrated Spin-1/2 Antiferromagnets

“…33,34,35,36 Some possible physical realizations are SrCrGaO or various jarosites which have kagomé planes of magnetic ions. 31,32 Fig 1d shows the spectrum of the N = 36 sample of the kagomé antiferromagnet.…”