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Springer proceedings in physics

Haldane Antiferromagnet in a Magnetic Field

Tôru Sakai, Masahiro Takahashi

Published Jan 1, 1992• 0 citations
Publisher
DOI
10.1007/978-3-642-84821-6_28

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Abstract In this paper a self‐consistent mean‐field approximation is used to study the thermodynamic properties of a spin‐1 antiferromagnetic Heisenberg chain with an anisotropy in the presence of an external magnetic field at a finite temperature. The temperature dependences of the internal energy, Haldane gap, and correlation length are presented. It is found that the internal energy and Haldane gap increase with increasing temperature, while the correlation length decreases for a fixed magnetic field and single‐ion anisotropy. The magnetic field splits the Haldane gap into two branches: the upper branch increases with increasing magnetic field while the other branch decreases. The numerical results are consistent with those of other theoretical methods. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)•Nov 25, 2003•1 citation
The author studies the S=1 antiferromagnetic Heisenberg chain with uniaxial anisotropy, which exhibits the Haldane gap phenomenon. He argues that, when a magnetic field in a direction transverse to the anisotropy axis is applied, a sharp phase transition takes place at a critical value of the field. The transition is characterized by vanishing of the hidden antiferromagnetic order which can be measured by the string order parameter of den Nijs and Rommelse. The existence of such a transition distinguishes a Haldane gap system from other disordered quantum spin systems.
The behavior of Haldane-gap antiferromagnets in a strong magnetic field is not universal. While the low-energy physics of the conventional one-dimensional spin-1 Heisenberg model in its magnetized regime is described by one incommensurate soft mode, other systems with somewhat perturbed coupling constants can possess two characteristic soft modes in a certain range of the field strength. Such a two-component Luttinger liquid phase is realized above the massive Haldane-gap phase, and in general above any massive nonmagnetic phase, when the ground state exhibits short-range incommensurate fluctuations already in the absence of the field.
Abstract In this paper a self‐consistent mean‐field approximation is used to study the thermodynamic properties of a spin‐1 antiferromagnetic Heisenberg chain with an anisotropy in the presence of an external magnetic field at a finite temperature. The temperature dependences of the internal energy, Haldane gap, and correlation length are presented. It is found that the internal energy and Haldane gap increase with increasing temperature, while the correlation length decreases for a fixed magnetic field and single‐ion anisotropy. The magnetic field splits the Haldane gap into two branches: the upper branch increases with increasing magnetic field while the other branch decreases. The numerical results are consistent with those of other theoretical methods. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)