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Physical review. B, Condensed matter

Finite-temperature properties of the planar ferromagnetic xxz chain

Ueli Glaus, T. Schneider, E. Stoll

Published Jun 1, 1983• 4 citations
Publisher

Abstract

We present analytic weak-coupling and numerical finite-chain results for the specific heat, the longitudinal zero-field susceptibility, and the longitudinal dynamic form factor of the planar ferromagnetic $\mathrm{xxz}$ chain at finite temperatures. It is shown that the "bound state" probed by the dynamic form factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ within the Hartree-Fock approximation has to be interpreted as the first moment of ${S}_{\mathrm{zz}}$ of the states lying above the continuum appearing in the isotropic $\mathrm{xy}$ model.

DOI
10.1103/physrevb.27.6770

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We present analytic weak-coupling and numerical finite-chain results for the specific heat, the longitudinal zero-field susceptibility, and the longitudinal dynamic form factor of the planar ferromagnetic xxz\mathrm{xxz}xxz chain at finite temperatures. It is shown that the "bound state" probed by the dynamic form factor Szz(q,\ensuremathω){S}_{\mathrm{zz}}(q,\ensuremath{\omega})Szz​(q,\ensuremathω) within the Hartree-Fock approximation has to be interpreted as the first moment of Szz{S}_{\mathrm{zz}}Szz​ of the states lying above the continuum appearing in the isotropic xy\mathrm{xy}xy model.
We present analytic weak-coupling and numerical finite-chain results for the dynamic form factor associated with the out-of-plane fluctuations at zero temperature and zero field. The dynamic form factor associated with the in-plane fluctuations is treated numerically only. In the ferromagnetic regime, the dominant features are traced back to particle-hole pair continua and the associated bound states. With the approach toward the isotropic ferromagnet, the resonance associated with the bound state of the particle-hole pairs gradually exhausts the spectrum, corresponding in this limit to the magnon peak. In the antiferromagnetic regime, the spectrum is dominated by the particle-hole pair continuum. The analytic results for the dynamic form factor associated with the out-of-plane fluctuations reproduce and extend the well-known properties of the continuum model to leading order in the coupling constant. As expected from the relation between the six-vertex model and the xxz\mathrm{xxz}xxz chain, these properties include singular behavior of dynamic form factors depending continuously on the coupling constant.
Results are presented and interpreted for the zero- and finite-temperature excitation spectrum of ferromagnetic Ising-Heisenberg chains, as probed by dynamic form factors. Finite-chain calculations demonstrate the occurrence of a thermally induced resonance centered around zero frequency, and a broadening of the magnon and two-magnon bound-state resonances at low TTT. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.
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.
The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.
The excitation spectrum of the ferromagnetic s=12s=\frac{1}{2}s=21​ Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with s>12s>\frac{1}{2}s>21​, such as CsNiF3{\mathrm{F}}_{3}F3​, and on the soliton aspect of the classically treated systems.