Eur. Phys. J. B 31, 63-67 (2003)
https://doi.org/10.1140/epjb/e2003-00009-7

The extended spin ladder and net models: exact dimer ground state and quantum phase transition

¹ Institut für Theoretische Physik, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
² Institute of Physics, Chinese Academy of Science, PO Box 603, Beijing 100080, PR China

Corresponding author: ^a schen@thphy.uni.duesseldorf.de

Received: 13 October 2002
Published online: 27 January 2003

Abstract

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed.