Rigorous Solution of the Spin-1 Quantum Ising Model with Single-ion Anisotropy

Abstract

We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping it onto a series of segmented spin-1/2 transverse Ising chains, separated by the $S^z=0$ states called holes. A recursion formula is derived for the partition function to simplify the summation of hole configurations. This allows the thermodynamic quantities of this model to be rigorously determined in the thermodynamic limit. The low temperature behavior is governed by the interplay between the hole excitations and the fermionic excitations within each spin-1/2 Ising segment. The quantum critical fluctuations around the Ising critical point of the transverse Ising model are strongly suppressed by the hole excitations.

4 pages, 4 figures

References in corpus (8)

• Continuous Quantum Phase Transitions
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Effective quantum spin systems with ion traps
• Criticality in correlated quantum matter
• Site-Dilution in quasi one-dimensional antiferromagnet Sr2(Cu1-xPdx)O3: reduction of Neel Temperature and spatial distribution of ordered moment sizes
• 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

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