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Physical Review Letters

Excitation Spectrum and Thermodynamic Properties of the Ising-Heisenberg Linear Ferromagnet

James D. Johnson, J. C. Bonner

Published Mar 3, 1980• 28 citations
Publisher

Abstract

New analytic results are presented for the low-$T$ thermodynamics of the Ising-Heisenberg linear ferromagnetic in a magnetic field ${H}_{0}$. For small ${H}_{0}$ the thermodynamic functions show unexpected and interesting structure as a function of ${H}_{0}$ and the anisotropy $\ensuremath{\Delta}$. The thermal and magnetic energy gaps have singularities, not necessarily at the same $\ensuremath{\Delta}\ensuremath{-}{H}_{0}$ location, as changes occur in the type of excitation dominating the low-$T$ behavior. The results may relate to quantum solitons in the linear ferromagnet.

DOI
10.1103/physrevlett.44.616

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New analytic results are presented for the low-TTT thermodynamics of the Ising-Heisenberg linear ferromagnetic in a magnetic field H0{H}_{0}H0​. For small H0{H}_{0}H0​ the thermodynamic functions show unexpected and interesting structure as a function of H0{H}_{0}H0​ and the anisotropy \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ. The thermal and magnetic energy gaps have singularities, not necessarily at the same \ensuremathΔ\ensuremath−H0\ensuremath{\Delta}\ensuremath{-}{H}_{0}\ensuremathΔ\ensuremath−H0​ location, as changes occur in the type of excitation dominating the low-TTT behavior. The results may relate to quantum solitons in the linear ferromagnet.
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The thermodynamic properties of a spin S=1/2S=1/2S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating interactions AF1-AF2-AF1-F{\text{AF}}_{1}{\text{-AF}}_{2}{\text{-AF}}_{1}\text{-F}AF1​-AF2​-AF1​-F (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying JAF1=JAF2=JF{J}_{{\text{AF}}_{1}}={J}_{{\text{AF}}_{2}}={J}_{\text{F}}JAF1​​=JAF2​​=JF​ is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the S=1S=1S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.
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