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

Abstract

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.

11 pages, 9 figures, published version

References in corpus (9)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Criticality in Heavy Fermion Metals
• Continuous Quantum Phase Transitions
• A toolbox for lattice spin models with polar molecules
• Criticality in correlated quantum matter
• Designing spin-1 lattice models using polar molecules
• Chain breaks and the susceptibility of Sr_2Cu_{1-x}Pd_xO_{3+δ} and other doped quasi one-dimensional antiferromagnets
• A Theory of Ferroelectric Phase Transition in SrTiO${}_3$ induced by Isotope Replacement
• Rigorous Solution of the Spin-1 Quantum Ising Model with Single-ion Anisotropy

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• Local distributions of the 1D dilute Ising model
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• Quantum phase transitions in spin-1 compass chains
• The tensor renormalization group study of the general spin-S Blume-Capel model