Validity of the Lieb-Mattis theorem in the J(1)-J(2) Heisenberg model - art. no. 024403

摘要

The Lieb-Mattis theorem shows that, for the nonfrustrated spin-S Heisenberg antiferromagnet, the ground-state total spin is equal to N-A-N-BS, where N-A and N-B are the site numbers of two sublattices, respectively. For several J(1)-J(2) clusters, we calculate their ground-state total spins by exact diagonalization, and find that the conclusion of Lieb and Mattis is valid as long as Neel order exists. Frustrations which are not able to destroy Neel order cannot change the value of the ground-state total spin. Also, our calculations show that if the ground-state total spin does not abide by the conclusion of Lieb and Mattis, the ground state has no Neel order. For a J(1)-J(2) system of large enough size, those states which have total spins between N-A-N-BS and the lowest possible total spin are not able to become the ground state for arbitrary strength of frustration. To study the phase transition of the J(1)-J(2) model from Neel order to spin disorder, in some respects, the cluster with the geometric shape shown in this paper may be a better choice than usual nxn clusters since it can directly give the rather accurate critical ratio J(2)/J(1). References: 27