SOLUTIONS OF THE YANG-BAXTER EQUATION FOR ISOTROPIC QUANTUM SPIN CHAINS

We consider solutions of the Yang-Baxter equation such that the logarithmic derivative of the transfer matrix yields a quantum spin Hamiltonian which is isotropic in spin space, i.e. SU(2)-invariant. Four such solutions are known for each value of the spin S. (For S = 1/2 they degenerate into the same solution, and for S = 1 they only give three different solutions.) For S less-than-or-equal-to 6 we show that these are the only solutions which are SU(2)-invariant, except for S = 3 when there is a fifth solution.