Ordering Energy Levels of Interacting Spin Systems

TLDR

The total spin S is a good quantum number in interacting spin systems. The study investigates the structure of the lowest eigenfunctions in an external magnetic field. The authors define the total spin S as the absolute difference between the maximum spins of the two sublattices, SA and SB. For general antiferromagnetic or ferrimagnetic Hamiltonians, the lowest energy eigenvalue E(S) increases monotonically with S, with E(S+1)>E(S) for S≥0 in antiferromagnets and for S≥S in ferrimagnets, and the ferrimagnetic ground state lies at S≤S.

Abstract

The total spin S is a good quantum number in problems of interacting spins. We have shown that for rather general antiferromagnetic or ferrimagnetic Hamiltonians, which need not exhibit translational invariance, the lowest energy eigenvalue for each value of S [denoted E(S) ] is ordered in a natural way. In antiferromagnetism, E(S + 1) > E(S) for S ≥ 0. In ferrimagnetism, E(S + 1) > E(S) for S≥S, and in addition the ground state belongs to S≤S. S is defined as follows: Let the maximum spin of the A sublattice be SA and of the B sublattice SB; then S≡|SA−SB|. Antiferromagnetism is treated as the special case of S=0. We also briefly discuss the structure of the lowest eigenfunctions in an external magnetic field.