EXACT RESULTS ON THE DIMERIZATION TRANSITION IN SU(N) ANTIFERROMAGNETIC CHAINS

The author shows that SU(n) antiferromagnetic chains (or equivalently SU(2) spin-s-chains with Hamiltonians which project out singlet states) are exactly equivalent to the n2-state quantum Potts chain (obtained from the transfer matrix for the 2D classical Potts model), for arbitrary n (or s with n=2s+1). This implies that the models are spontaneously dimerised with a finite gap for n<2 but have a unique ground state and vanishing gap for n<or=2. The n to 0 limit may have some bearing on the quantum-Hall-effect localisation transition.