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Journal of Changshu Institute of Technology

Thermodynamic properties in spin-Peierls chain

Xue Jiang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Combining the thermal coherent states with the bosonization technique,we develop a self_consistent quantum approach to investigate the dimerized antiferromagnetic Heisenberg chain at finite temperature.In the case of weak dimerization,temperature dependences of the magnetic excited energy gap and the specific heat are calculated analytically.The energy gap monotonically decreases with increasing temperature until it vanishes at the Peierls transition temperature T_P.The specific heat is strongly enhanced near T_P.It is also found that there is a scaling behavior of T_P as a function of the zero_temperature dimerization δ_0 as T_P ∝δ~v_0 with v=(0.66) for small δ_0.Our results are qualitatively consistent with experimental data observed in CuGeO_3.

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Combining the thermal coherent states with the bosonization technique,we develop a self_consistent quantum approach to investigate the dimerized antiferromagnetic Heisenberg chain at finite temperature.In the case of weak dimerization,temperature dependences of the magnetic excited energy gap and the specific heat are calculated analytically.The energy gap monotonically decreases with increasing temperature until it vanishes at the Peierls transition temperature T_P.The specific heat is strongly enhanced near T_P.It is also found that there is a scaling behavior of T_P as a function of the zero_temperature dimerization δ_0 as T_P ∝δ~v_0 with v=(0.66) for small δ_0.Our results are qualitatively consistent with experimental data observed in CuGeO_3.
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 self-consistent quantum-theoretical analysis of the ground-state energy and low-energy excitation spectrum of a dimerized and frustrated Heisenberg chain by the bosonization representation in the continuum-limit approach. The frustration effects on the ground-state energy and energy gap are investigated for α>αc where α is the frustration parameter and αc is its critical value, above which a frustration-induced energy gap is opened. It is shown that as α increases, the ground-state energy decreases and the energy gap increases. We find that the dimerization dependence of the ground-state energy and energy gap for small dimerization obeys the Cross-Fisher power law only at α = αc, but departs significantly from it when α>αc. The present results are in good agreement with numerical analyses from the density-matrix renormalization-group and exact diagonalization methods. The relevance of our calculated results to recent experiments on the spin-Peierls compounds CuGeO3 is also discussed.
By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)(2)P(2)O(7), the effects of two energy scales of the weakly dimerized antiferromagnetic S=1/2 Heisenberg chain are explored. The low-energy scale, given by the spin gap Delta, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing the density-matrix renormalization-group approach for transfer matrices calculations, shows that this feature originates from changes in the magnetic entropy with respect to Delta, partial differentialS(m)/partial differentialDelta. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit, where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in Delta.
Thermodynamic properties of S =1 antiferromagnetic Heisenberg chains with free and periodic boundaries are investigated by means of a quantum Monte Carlo method. The specific heat is shown to have a peak at a temperature T peak ∼2Δ, where Δ is the energy gap of the present model, although global shape of the temperature dependence is very similar to the Schottky type specific heat. In open chains, due to the four-fold degeneracy of the ground state, the magnetic susceptibility shows a Curie-like divergence regardless of the number of spins. The extracted diverging part is consistent with the edge moment S =1/2.