Residual entropy and spin gap in a one-dimensional frustrated antiferromagnet
Résumé
We show that the low-energy sector of the S=1/2, antiferromagnetic Heisenberg model on a one dimensional lattice of coupled tetrahedra consists of 2N replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: (i) there is a residual ground-state entropy per spin equal to (1/4)ln 2; (ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.