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.

We demonstrate the possibility of creating and controlling an ideal and trimerized optical Kagomé lattice, and study the low temperature physics of various atomic gases in such lattices. In the trimerized Kagomé lattice, a Bose gas exhibits a Mott transition with fractional filling factors, whereas a spinless interacting Fermi gas at 2/3 filling behaves as a quantum magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half-filling for both components represents a frustrated quantum antiferromagnet with a resonating-valence-bond ground state and quantum spin liquid behavior dominated by a continuous spectrum of singlet and triplet excitations. We discuss the method of preparing and observing such a quantum spin liquid employing molecular Bose condensates.

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin- 1 / 2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low-temperature magnetothermal effect is associated with the existence of low-lying fluctuating singlets, but also that the whole picture ( T2 behavior of C(v) and the thermally activated spin susceptibility) implies contribution of both nonmagnetic and magnetic excitations. Comparison with experiments is made.

We study the ground state properties of the S= 1 2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (αJ) couplings. Classically, this system is known to be ordered in a 120 • Néel type state for values −∞ < α ≤ 1/8 of the ratio α of these couplings and in a collinear state for 1/8 < α < 1. The order parameter M and the helicity χ of the 120 • structure are obtained by numerical diagonalisation of finite periodic systems of up to N = 30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region −∞ < α < 1/8. It appears that the SW theory is still valid for the simple triangular HAF (α = 0) although the sublattice magnetisation M is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameter N of the collinear order support the previous conjecture of a first order transition between the 120 • and the collinear order at α ≃ 1/8.

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length ξ, the susceptibility at the ordering wavevector χ(Q), and the spin stiffness ρ clearly reflects the existence of two temperature regimes -a high temperature regime T > T th , in which the disordering effect of vortices is dominant, and a low temperature regime T < T th , where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For T > T th , a satisfactory fit of the data is achieved, if the temperature dependence of ξ and χ(Q) is assumed to be of the form predicted by the Kosterlitz-Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around T th ≃ 0.28.