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Journal of Physics C Solid State Physics

The magnetic field dependence of the specific heat in quantum spin chains with axial symmetry

N. Papanicolaou, P Spathis

Published Oct 20, 1987• 8 citations
Publisher

Abstract

The magnetic specific heat in a class of spin- 1 / 2 chains with uniaxial anisotropy is determined accurately by a numerical solution of certain integral equations derived earlier through the Bethe ansatz. The specific heat exhibits a characteristic double peak as a function of an applied magnetic field which cannot be accounted for by the spin wave approximation. This illustrates the importance of non-linearity for the thermodynamics of quantum spin chains even at low temperature.

DOI
10.1088/0022-3719/20/29/005

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The magnetic specific heat in a class of spin- 1 / 2 chains with uniaxial anisotropy is determined accurately by a numerical solution of certain integral equations derived earlier through the Bethe ansatz. The specific heat exhibits a characteristic double peak as a function of an applied magnetic field which cannot be accounted for by the spin wave approximation. This illustrates the importance of non-linearity for the thermodynamics of quantum spin chains even at low temperature.
We consider an exactly solvable two-chain quantum spin- model in a generalized form with enhanced spin frustration. This model is exactly diagonalized via Bethe's ansatz. The low-temperature specific heat of the system is obtained with and without a magnetic field, using the thermodynamic Bethe ansatz equations. We also calculate the magnetic susceptibility in a sufficiently weak field, yielding typical logarithmic corrections. The spin frustration affects only the amplitudes in the magnetic susceptibility and the specific heat. This extends the previous results for a simple two-chain quantum spin model to the generalized one.
The authors present calculations of the specific heat of 1D quantum spin chains for a number of integrable and non-integrable Hamiltonians, in the presence of a magnetic field. For S=1 the Hamiltonian has both bilinear and biquadratic isotropic exchange and includes ferromagnetic and antiferromagnetic versions of the Heisenberg, Takhtajan-Babujian (TB), Lai-Sutherland (LS) (permutation) and biquadratic models. The two methods used are (i) direct numerical diagonalisation for chains of up to nine atoms and (ii) numerical solution of the Bethe ansatz equations for the integrable models (TB and LS). Generalisations of the latter method to S>1 are also given. For the integrable models the two methods give results in good agreement. Various types of behaviour, particularly at low T, are found and these are related to known phase changes at T=0. The results of the first method for the non-integrable Hamiltonians are discussed with reference to the existence of the Haldane gap in the S=1 Heisenberg model and a possible gap in the biquadratic model.
Earlier work on the T=0T=0T=0 dynamics of spin-1 chains with a strong easy-plane anisotropy is extended to include thermodynamics. Thus we carry out a systematic strong-coupling expansion to obtain analytical approximations for the spectrum of elementary excitations, the specific heat, and the magnetic susceptibility. Comparison with numerical data for the specific heat available in some important special cases indicates that our result is accurate for practically the entire temperature range. Similarly our calculation of the magnetic susceptibility reproduces to leading order a result obtained earlier through a molecular-field approximation and provides a definite improvement by including the two-loop correction. These theoretical predictions are directly relevant for a number of magnetic materials of current experimental interest.
We calculate exactly the thermodynamics of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the critical region of the uniaxial spin-1/2 quantum chain. We derive a finite set of integral equations describing the complete temperature and magnetic field dependence of the system. Exact numerical results for arbitrary values of temperature and external magnetic field are obtained. We show that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with a critical non-Fermi-liquid behaviour of the magnetic susceptibility and specific heat. We point out that the `easy-plane' magnetic anisotropy does not qualitatively change the behaviour of the thermodynamic characteristics of the disordered impurities in the antiferromagnetic chain. On the other hand, anisotropy of ferromagnetic type can enhance the tendency to quenching of the impurities for strong disorder.