SINGLET GROUND STATE OF THE BILINEAR-BIQUADRATIC EXCHANGE HAMILTONIAN

摘要

We show that the ground state of the bilinear-biquadratic exchange Hamiltonian is always singlet on a connected finite lattice with an even number of sites, while it is always triplet on one with an odd number of sites, if coefficients of the bilinear term -J and that of the biquadratic term -J' satisfy the condition J'>J>0. We also find that the total-spin eigenvalue S-tot of the lowest-energy state in each subspace classified by M, an eigenvalue of z component of the total spin, depends on the parity of M, i.e, S-tot = M for even M and S-tot = M + 1 for odd M on an even number site lattice and vice versa on an odd number site lattice. [S0163-1829(97)04941-2]. [References: 23]