Ground-State Properties of Finite Antiferromagnetic Chains

Exact calculations are presented for the ground state of linear antiferromagnetic Heisenberg chains with open ends. The wave function and the energy are given for chains with N = 4, 6, and 8, and quantum number S = 1/2. It is shown that in the limit for N - ∞ the ground state is probably nondegenerate and the long-range order tends to zero. The short-range order shows a strongly oscillating character due to end effects persisting over relatively long distances. A comparison with closed rings is made and the connection with the observation of a reduction of the zero-point deviation in the neighbourhood of non-magnetic impurities in more-dimensional systems is pointed out.