Exact solutions of a class of S=1 quantum Ising spin models

Details Exact solutions of a class of S=1 quantum Ising spin models Exact solutions of a class of S=1 quantum Ising spin models

2008-11-14

arxiv.org/abs/0811.2275v2

Phys. Rev. B 79, 214427(2009)

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, 9 figures, published version

Scientific paper

10.1103/PhysRevB.79.214427

We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising models, characterized by the total number of holes. A recursion formula is derived for the partition function based on the reduced $S=1/2$ Ising model. This simplifies greatly the summation over all the hole configurations. It allows the thermodynamic quantities to be rigorously determined in the thermodynamic limit. The ground state phase diagram is determined for both the uniform and dimerized spin chains. The corresponding thermodynamic properties are calculated and discussed.

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