Coupled cluster treatment of one quasi-one-dimensional coupled spin triangles

By using the coupled cluster method (CCM) and the numerical exact diagonalization (ED) method, we investigated the properties of the one quasi-one-dimensional coupled spin triangles. The results of ED disclose that the system is in the exact tetramer-dimer (TD) state if a<ac1 . We prove that the exact TD state can be formed by using CCM in that parameter region. It is more interesting to find that the exact spin gap in the TD state can also be obtained via CCM. At the critical point ac1, a first order transition occurs and the ground state of the system evolves from the TD state to the ferromagnetic long range order state. In the parameter region a>ac1, we find that CCM results for some physical quantities, such as the ground state energy, the magnetization and the antiferromagnetic gap are in excellent agreement with the results obtained by ED. Thus, CCM can be used to accurately analyze the properties of the quasi-one-dimensional coupled spin triangles in the whole parameter region. We believe that it can also be applied to investigating the properties of other quasi-one spin systems reliably.
Comment: This paper has been withdrawn by the author due to a error in equation 8