Heisenberg spin chains: Quantum-classical crossover and the Haldane conjecture

A comprehensive investigation has been made of the spectral excitations and static properties of Heisenberg antiferromagnetic chains of spin 1/2, 1, 3/2, and 2, using Lanczös, Bethe Ansatz, and Monte Carlo techniques. An unusual and unanticipated crossover mechanism for spin chains with 1/2≤S≤∞ has been discovered. The validity of the Haldane conjecture concerning the presence of a spectral excitation gap for integer-spin chains has been investigated by exact finite chains calculations of (a) the primary singlet-triplet excitation gap, (b) higher excitation gaps, and (c) the Fourier transform of the ground state correlation functions. A new Monte Carlo method has extended the spin-1 gap calculations to N=32.