Anisotropic Heisenberg chain with composite spin

Abstract

A family of one-dimensional magnetic Hamiltonians is introduced, where at each site there are $n$ spin-$S$ operators. It is shown that, for special couplings between spins and for $S=\frac{1}{2}$, the model contains the complete spectrum of the Heisenberg chain with spins ½, 1, frac32;, etc., and the ground state is that of the corresponding Heisenberg chain. By the varying of a single parameter the model allows continuous transitions between chains with different spin. We map the spin-($S+S$) model onto the nonlinear $\sigma$ model and discuss the possibility of a finite gap in the spin-(½+½) model.