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Chinese Physics Letters

Villain Transformation for Ferrimagnetic Spin Chain

Ge Yang, Bin Chen

Published Jun 1, 2014• 1 citation
Publisher

Abstract

By using the Villain transformation, the Heisenberg ferrimagnetic spin chain is calculated. Two branches of the low-lying excitation in both the absence and presence of magnetic field are obtained. The thermodynamic quantities (such as free energy, magnetization, specific heat and static magnetic susceptibility) are also evaluated at finite temperature. This is the first time to calculate the Ferrimagnetic spin chain by using Villain's method, and we find that the results at a low temperature are quite similar to the previous calculation. The results of free energy and magnetization in zero temperature suggest that the Villain transformation has a good efficiency.

DOI
10.1088/0256-307x/31/6/060506

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By using the Villain transformation, the Heisenberg ferrimagnetic spin chain is calculated. Two branches of the low-lying excitation in both the absence and presence of magnetic field are obtained. The thermodynamic quantities (such as free energy, magnetization, specific heat and static magnetic susceptibility) are also evaluated at finite temperature. This is the first time to calculate the Ferrimagnetic spin chain by using Villain's method, and we find that the results at a low temperature are quite similar to the previous calculation. The results of free energy and magnetization in zero temperature suggest that the Villain transformation has a good efficiency.
The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T=0K.T=0 \mathrm{K}.T=0K. These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at T>0K,T>0 \mathrm{K},T>0K, are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.
Energy spectra and thermodynamic quantities (partition function, entropy, specific heat, susceptibility) of ferrimagnetic Heisenberg chains, made up of two spin sublattices [(1/2-S], are discussed from the exact results computed for finite rings. Extrapolation of the theoretical data versus the length of finite rings N is discussed for S ranging from 1 to (5/2 and compared with previous reported findings for the [(1/2-\ensuremath{\infty}] spin chain. In the low-temperature region, similarities between the ferrimagnetic chains [(1/2-S] and the regular ferromagnetic ones (with spin S-(1/2) are used for the determination of the limiting curves.
We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic (S=5∕2S=5∕2S=5∕2, s=2s=2s=2) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field-dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat, and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin-wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin-wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.
The low-energy structures of the quantum ferrimagnetic Heisenberg chain consisting of (5/2, 1/2, 1/2) trimers are investigated theoretically. The results of the linear spin-wave theory are compared with those from the numerical exact diagonalization calculation and the matrix product method for the lowest optical mode. The temperature behaviour of thermodynamical properties such as magnetic susceptibility, specific heat and entropy are analysed in the framework of the modified spin-wave theory. The results of the calculations are used to explain the experimental data obtained for the molecule-based heterospin magnets [Mn(hfac) 2 BNO R ] (R = H, F, Cl, Br) with one-dimensional chain structure.
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.
Quantum phase transitions in alternating spin-(12\frac{1}{2}21​, 52\frac{5}{2}25​) Heisenberg chains
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.