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Chinese Physics Letters

Specific Heat of the Spin-1/2 Antiferromagnetic Heisenberg Chain

Guohong Yun, Liang Xi-Xia

Published Aug 16, 2001• 3 citations
Publisher

Abstract

A simple analytic theory of thermodynamics at finite temperature for the spin-1/2 antiferromagnetic Heisenberg chain is proposed based on the picture of the particle-hole pair excitations. The dispersion relation of the particle-hole pairs is derived in the formulation of thermodynamic Bethe ansatz provided that the particles and holes have the same energy and they are excited as normal modes. It is shown that the behaviour of the specific heat is in excellent agreement with the numerical and experimental results.

DOI
10.1088/0256-307x/18/9/335

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A simple analytic theory of thermodynamics at finite temperature for the spin-1/2 antiferromagnetic Heisenberg chain is proposed based on the picture of the particle-hole pair excitations. The dispersion relation of the particle-hole pairs is derived in the formulation of thermodynamic Bethe ansatz provided that the particles and holes have the same energy and they are excited as normal modes. It is shown that the behaviour of the specific heat is in excellent agreement with the numerical and experimental results.
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The one-dimensional spin-1 Heisenberg antiferromagnetic chains are studied by a generalized two-time Green's-function method at finite temperature. 〈Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​〉 is set to zero at each site to guarantee the lack of the long-range order in the one-dimensional Heisenberg system. The Green's functions are decoupled in terms of the correlation functions of spin operators. A set of self-consistent equations of the correlation functions are derived and solved numerically. Correlation functions of spin operators, thermodynamic properties such as the internal energy, and specific heat in the entire temperature region are obtained. The Haldane gap in the excitation spectrum appears naturally in the analytical result. When k is zero, there is a gap 2\ensuremath{\Delta}, which is 1.0J and close to the theoretical result of White and Huse. And there is a broad maximum in the temperature dependence of the specific heat. The properties of the thermodynamic quantities are consistent with the numerical results on the finite chains. \textcopyright{} 1996 The American Physical Society.
We present a new application of the traditional thermodynamic Bethe ansatz to the spin-1/2 antiferromagnetic uniform Heisenberg chain and derive exact nonlinear integral equations for just two functions describing the elementary excitations. By using this approach, the magnetic susceptibility chi and specific heat C versus temperature T are calculated to high accuracy for 5x10(-25)</=T/J</=5. The chi(T) data agree very well at low T with the asymptotically exact theoretical low- T prediction of Lukyanov [Nucl. Phys. B522, 533 (1998)]. The unknown coefficients of the second and third lowest-order logarithmic correction terms in Lukyanov's theory for C(T) are estimated from the C(T) data.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
Elementary excitations for the integrable spin-S antiferromagnetic Heisenberg chain with an impurity spin are investigated by using the Bethe ansatz solution. Dressed holes are introduced in order to describe the elementary excitation. The characteristic energy dependence of the spectral density for the elementary excitation at zero temperature is discussed in connection with behaviour patterns of physical quantities. We extend our calculation for the elementary excitation to the case of finite temperatures, applying the method developed by Yang and Yang for one-dimensional interacting boson systems. At finite temperatures, in the case where , the spectral density shows a divergence property at zero excitation energy irrespective of the temperature, whereas in the case where , the peak structure develops in the low-energy region as the temperature is decreased.