Starting from a modified version of the the S=1/2 Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the quantum nature of these variables is shown to yield a Hamiltonian that can be solved exactly, leading to the following predictions: i) The number of low lying singlet states increase with the number of sites N like 1.15 N ; ii) A singlet-triplet gap remains in the thermodynamic limit; iii) Spinons form boundstates with a small binding energy. By comparing these properties with those of the regular Kagome lattice as revealed by numerical experiments, we argue that this description captures the essential low energy physics of that model.

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase ($H_c^1$, $H_c^2$, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.Comment: One mistake corrected, one reference adde

We show that the factorized wave-function of Ogata and Shiba can be used to calculate the k dependent spectral functions of the one-dimensional, infinite U Hubbard model, and of some extensions to finite U . The resulting spectral function is remarkably rich: In addition to low energy features typical of Luttinger liquids, there is a well defined band, which we identify as the shadow band resulting from 2kF spin fluctuations. This band should be detectable experimentally because its intensity is comparable to that of the main band for a large range of momenta. 71.10.Fd, 78.20.Bh The calculation of the spectral functions of models of correlated electrons is one the most challenging and largely unsolved issues of condensed matter theory. Although a number of numerical techniques can be used, e.g. exact diagonalization of finite clusters [1] or quantum Monte Carlo simulations [2], exact results are available only in very special cases, mostly for one-dimensional spin models [3]. As far as one-dimensional electron models are concerned, most of the well established results have been obtained in the framework of the Luttinger liquid theory [4,5,6,7], which is believed to be the correct description of the low energy properties of a large class of Hamiltonians. However, an accurate determination of the dynamical properties for all frequencies is so far still lacking.In this paper we perform such a calculation for the following one-dimensional models:i) The Hubbard model defined by the Hamiltonianin the infinite U limit, which is also equivalent to the J → 0 limit of the standard t − J model; ii) An extension of the t − J model first proposed by Xiang and d'Ambrumenil

We study the occurrence of plateaux and jumps in the magnetization curves of a class of frustrated ladders for which the Hamiltonian can be written in terms of the total spin of a rung. We argue on the basis of exact diagonalization of finite clusters that the ground state energy as a function of magnetization can be obtained as the minimum -with Maxwell constructions if necessaryof the energies of a small set of spin chains with mixed spins. This allows us to predict with very elementary methods the existence of plateaux and jumps in the magnetization curves in a large parameter range, and to provide very accurate estimates of these magnetization curves from exact or DMRG results for the relevant spin chains.