Ground states and excitations of a one-dimensional kagome-like antiferromagnet

We study a Heisenberg antiferromagnet (AF) on a one-dimensional strip compo sed of two rows of corner sharing triangular plaquettes. The geometry of th is ladder-like lattice naturally allows for two different exchange coupling s, one between pairs of spins on the outer legs (J) and a different one bet ween the spies on the axis and their nearest neighbors on the legs (J'). Fo r J/J' less than or similar to 0.5 the model is a ferrimagnet. Our main int erest is in the region J/J' greater than or similar to 0.5, when the classi cal ground state of this system shows the same macroscopic degeneracy as th e classical ground state of the antiferromagnet on the kagome lattice. To e xplore to which extent this similarity between the classical ground states of these two models carries over to their quantum states we have applied ex act diagonalization techniques and density-matrix renormalization group (DM RG) methods to our model. Exact diagonalization is restricted to system siz es of up to N = 30 sites. Fur J/J' = I, the results obtained by this techni que, low-energy spectra, correlation functions and the specific heat, agree qualitatively with the results obtained for finite samples of the kagome A F. As in the case of the kagome AF, these finite size results suggest that our model is a spin liquid with a gap between the ground state and the lowe st spin excitation. However, extrapolations from DMRG data far strips of up to N = 120 sites point towards a vanishing spin gap in a wide range of cou plings, 0.5 less than or similar to J/J' less than or similar to 1.25, so t hat contrary to the above conjecture, our one-dimensional model may in fact be critical in this parameter range. Moreover, our DMRG data indicate that the model undergoes a transition to a gapped state as the ratio J/J' incre ases through the value J/J' = 1.25. In the vicinity of the transition point , a high density of low-lying singlets develops in the spin gap.