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physica status solidi (b)

Thermodynamic properties of a spin‐1 antiferromagnetic chain with an anisotropy at a finite temperature

Jialiang Li, Suhua Zhu

Published Nov 25, 2003• 1 citation
Publisher

Abstract

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)

DOI
10.1002/pssb.200301893

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Physical review. B, Condensed matter•Nov 1, 1993•12 citations
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)
We study the low-temperature properties of a spin-1 Heisenberg antiferromagnetic chain in an external magnetic field by an extended self-consistent mean-field approach developed earlier based on Anderson's spin-wave theory. At fixed magnetic field, the excitation energies increase, while the correlation length decreases with the increasing temperatures. The magnetic field leads to the Zeeman splitting of the excitations with the upper branch going up and the lower branch going down with the increasing fields. At zero temperature the correlation length is a constant and the gap closes at a critical magnetic field, while at finite temperature the correlation length decreases and a small gap seems to survive at the critical magnetic field. These results are consistent with those of other theoretical studies and agree with the experiments quite well. Also, we show that the system shares very similar properties with the valence-bond-solid state even at finite temperatures. The magnetization is studied and the coexistence of the hidden long-range order and the field-induced ferromagnetic order is discussed.
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.
Abstract We employed the classical transfer matrix technique to investigate the magnetization and quadrupolar plateaus, phase diagrams and other thermodynamical properties of the one‐dimensional antiferromagnetic spin‐3/2 and spin‐2 Blume–Capel model in the presence of an external magnetic field at very low temperatures. We showed that single‐ion anisotropy is one of the indispensable ingredients for an energy gap which causes to magnetization and quadrupolar plateaus in one‐dimensional antiferromagnetic Ising spin chains. Other thermodynamical predictions seem to be provide this argument. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
By the numerical transfer-matrix method we have computed several thermal properties for a Heisenberg chain of 150 antiferromagnetically coupled spins with quantum number s = 1. We dispensed with any extrapolation to the infinite chain, because the results for the magnetization, the susceptibility, the correlation length, and the static structure factor at wave number q = π have been found to be insensitive to a further increase of the chain length in the temperature regime considered. The characteristic features of our results, that occur at sufficiently low temperatures and low applied fields, can convincingly be explained by the existence of a gap in the excitation spectrum of the order of 0.4 coupling constants and, therefore, nicely complement previous numerical results for corresponding ground-state properties. We have also performed computations for a chain with an additional single-site anisotropy. We find, for appropriate parameter values, excellent agreement with experimental data for the quasi-one-dimensional model compound NENP.
Thermodynamic properties of S=1 antiferromagnetic Heisenberg chains with free and periodic boundaries are investigated by a quantum Monte Carlo method. In particular, temperature dependences of the specific heat, the magnetic susceptibility, and the hidden order parameter, which are inherent to the Haldane phase, are investigated. The specific heat turns out to have a peak at a temperature Tpeak{\mathit{T}}_{\mathrm{peak}}Tpeak​\ensuremath{\sim}2\ensuremath{\Delta}, where \ensuremath{\Delta} is the energy gap of the present model, although the temperature dependence of the specific heat is very similar to the Schottky type. In open chains, due to the fourfold degeneracy of the ground state, the magnetic susceptibility shows a Curie-like divergence regardless of the number of spins in the chain. The amplitude of the Curie-like divergence is consistent with the edge moments (S=1/2). On the other hand, it is confirmed that the long-range hidden order exists only in the ground state. How the hidden order grows as the temperature goes to zero (T\ensuremath{\rightarrow}0) is investigated by introducing an intrinsic correlation length ${\ensuremath{\xi}}_{\mathit{D}}$ of the ordering, which diverges as T\ensuremath{\rightarrow}0. A qualitative difference in fluctuations between the ground state and the finite-temperature states is discussed making use of snapshots of the transformed two-dimensional Ising system on which a Monte Carlo simulation is being performed.
A spin-1 antiferromagnetic Heisenberg chain with a single-ion anisotropy Dtsumj{\mathit{Dtsum}}_{\mathit{j}}Dtsumj​(Sjz{\mathit{S}}_{\mathit{j}}^{\mathit{z}}Sjz​)2{)}^{2})2 is investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the ground state, the excitation spectrum, and the correlation functions are derived in a self-consistent-field approach. We find that the ground state is made of boson pairs and the correlation functions in the ground state decay exponentially. Two Haldane gaps due to the single-ion anisotropy are obtained and a transition at the critical value Dc{\mathit{D}}_{\mathit{c}}Dc​=1 is shown in the lower Haldane gap and the correlation functions.