Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Abstract

Some rigorous results are presented for a first-order quantum phase transition between the dimerized state and Haldane-type state (i.e., a state similar to the ground state of the one-dimensional spin-1 Heisenberg chain) in the spin-1/2 coupled chains with nearest-neighbour and next-nearest-neighbour Heisenberg interactions. Also presented are the exact excited states in both phases. A partial phase diagram of the general spin-1/2 coupled chains is discussed.