Le Journal de Physique Colloques

NUMERICAL QUANTUM TRANSFER-MATRIX RESULTS FOR A SPIN CHAIN CORRESPONDING TO CHAB

Th. Delica, R. W. Gerling, Hajo Leschke

Published Dec 1, 1988• 1 citation

Abstract

A variant of the quantum transfer-matrix method is used to obtain numerically accurate results for the specific heat of an easy-plane spin chain with an in-plane field, corresponding to the ferromagnetic compound CHAB. They are contrasted with predictions of the classical sine-Gordon approximation for the chain and with experimental data.

DOI: 10.1051/jphyscol:19888725

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Le Journal de Physique Colloques

NUMERICAL QUANTUM TRANSFER-MATRIX RESULTS FOR A SPIN CHAIN CORRESPONDING TO CHAB

Th. Delica, R. W. Gerling, Hajo Leschke

Published Dec 1, 1988• 1 citation

Publisher

Abstract

DOI: 10.1051/jphyscol:19888725

Related papers

New numerical transfer-matrix results for a quantum spin chain corresponding to ( C6 H11 N H3 ) Cu Br3 (CHAB)

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New numerical results for the specific heat of a quantum spin-chain model believed to be appropriate for ferromagnetic ( ${\mathrm{C}}_{6}$ ${\mathrm{H}}_{11}$ N ${\mathrm{H}}_{3}$ ) Cu ${\mathrm{Br}}_{3}$ (CHAB) are obtained by a variant of the numerical exact transfer-matrix method. While agreement is found with some predictions of the classifical sine-Gordon approximation of this model, the results disagree with previous numerical results and are inconsistent with experimental data for CHAB.New numerical results for the specific heat of a quantum spin-chain model believed to be appropriate for ferromagnetic (${\mathrm{C}}_{6}$${\mathrm{H}}_{11}$N${\mathrm{H}}_{3}$) Cu${\mathrm{Br}}_{3}$ (CHAB) are obtained by a variant of the numerical exact transfer-matrix method. While agreement is found with some predictions of the classifical sine-Gordon approximation of this model, the results disagree with previous numerical results and are inconsistent with experimental data for CHAB.

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Physical review. B, Condensed matterFeb 1, 19853 citations

New numerical results for the specific heat of a quantum spin-chain model believed to be appropriate for ferromagnetic (

{\mathrm{C}}_{6}

{\mathrm{H}}_{11}

{\mathrm{H}}_{3}

) Cu

{\mathrm{Br}}_{3}

(CHAB) are obtained by a variant of the numerical exact transfer-matrix method. While agreement is found with some predictions of the classifical sine-Gordon approximation of this model, the results disagree with previous numerical results and are inconsistent with experimental data for CHAB.

{\mathrm{CsNiF}}_{3}

shows much improvement in the description of this system. In addition, new light is shed on the old problem of defining the classical counterpart of a spin Hamiltonian.

{\mathit{scrH}}_{\mathrm{eff}}

. We use the Villain transformation to canonical conjugate variables, in order to treat the quantum renormalizations within this framework. In the resulting effective Hamiltonian we restore classical spin variables, according to the classical counterpart of the Villain transformation. Provided that the quantum coupling parameter (which depends on the spin value and on the anisotropy constant) is not too large, this effective Hamiltonian is able to account for the quantum behavior, by means of classical-like calculations. We present a number of results for various quantum thermodynamic quantities, obtained numerically by the classical transfer-matrix method. Moreover, we also calculate static spin correlation functions. Finally, the case of the real ferromagnet

{\mathrm{CsNiF}}_{3}

is considered; even though the corresponding easy-plane anisotropy is rather weak, the experimental data for this system are shown to be well reproduced.

The quantum transfer-matrix method (QTM) has been applied to study the finite-temperature static properties of the spin

S=1

antiferromagnetic Heisenberg chains in a wide range of the single-ion anisotropy and temperatures. The high-resolution QTM simulation data are obtained for the zero-field susceptibility, specific heat, as well as for the field-dependent magnetization. The microscopic parameters of a number of real quasi-one-dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and low-temperature extensions of high-temperature series are given in terms of Chebyshev polynomials.