Validity of the LiebMattis theorem in the J_{1}J_{2} Heisenberg model
Abstract
The LiebMattis theorem shows that, for the nonfrustrated spinS Heisenberg antiferromagnet, the groundstate total spin is equal to N_{A}N_{B}S, where N_{A} and N_{B} are the site numbers of two sublattices, respectively. For several J_{1}J_{2} clusters, we calculate their groundstate total spins by exact diagonalization, and find that the conclusion of Lieb and Mattis is valid as long as Néel order exists. Frustrations which are not able to destroy Néel order cannot change the value of the groundstate total spin. Also, our calculations show that if the groundstate total spin does not abide by the conclusion of Lieb and Mattis, the ground state has no Néel order. For a J_{1}J_{2} system of large enough size, those states which have total spins between N_{A}N_{B}S 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 Néel order to spin disorder, in some respects, the cluster with the geometric shape shown in this paper may be a better choice than usual n×n clusters since it can directly give the rather accurate critical ratio J_{2}/J_{1}.
 Publication:

Physical Review B
 Pub Date:
 June 2002
 DOI:
 10.1103/PhysRevB.66.024403
 Bibcode:
 2002PhRvB..66b4403L
 Keywords:

 75.10.Jm;
 64.60.Cn;
 75.40.Mg;
 Quantized spin models;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Numerical simulation studies