In terms of spinless fermions and spin waves, we describe magnetic properties of a spin-1/2 ferromagnetic– antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On one hand, we employ the Jordan–Wigner transformation and treat the fermionic Hamiltonian within the Hartree–Fock approximation. On the other hand, we employ the Holstein– Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool to investigate one-dimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.
The excitation spectrum of the quantum antiferromagnetic Heisenberg model for a square lattice, as predicted from the in-phase flux state of Wigner-Jordan fermions, is calculated and compared with that calculated from conventional spin-wave theory. While the two spectra are overall similar, there are significant differences for short-wavelength excitations. The ratio of the excitation energy at wave vector (\ensuremath{\pi}/2,\ensuremath{\pi}/2) to that at (\ensuremath{\pi}/2,0) is predicted to be \ensuremath{\surd}2 for the Wigner-Jordan fermion excitations, and 2/ \ensuremath{\surd}3 for the spin-wave excitations. At long wavelengths, in contrast to the gapped spin-wave spectrum of Auerbach and Arovas, the excitation spectrum of Wigner-Jordan fermions is gapless at any finite temperature. Possible experimental examination of the excitation spectrum is discussed.
In terms of spinless fermions and spin waves, we describe the magnetic properties of a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On the one hand, we employ the Jordan–Wigner transformation and treat the fermionic Hamiltonian within the Hartree–Fock approximation. On the other hand, we employ the Holstein–Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool for investigating one-dimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.
The one-dimensional Heisenberg antiferromagnet with 8=1/2 is treated with the use of the Fermi operators and an additional condition that the long-range order is absent.Our spin wave spectrum of a one-dimensional Heisenberg antiferromagnet without longrange order is expressed by andThis is in good agreement with the exact spin wave spectrum role =1!'/2lsin kl which is obtained by des Cloizeaux and Pearson at T=O.Correlation functions <S1S2> and <SlSs> are in good agreement with the exact value at T=O, also.Thermodynamic properties of this system agree with those of Bulaevskii and those of Katsura and Inawashiro. § I. IntroductionThe one-dimensional Heisenberg antiferromagnet has been investigated by many authors.Most of previous theories have been for either zero or infinite temperatures.Recently various experiment on (CD3) 4NMnCl 3 (TMMC)ll requires further theoretical work of a Heisenberg linear-chain magnet for finite temperatures.The experimental results of linear antiferromagnet show that at low temperatures there are long-lived spin waves in spite of the absence of long-range order.At T= 0, the spin wave spectrum, wqoc I sin ql, is gained approximately by Anderson 2 l and exactly by des Cloizeaux and Pearson.8 l Recently Richards, 4 l Scales and Gersh, 5 l Kondo and Yamaji 6 l obtained the spin wave spectrum of linear antiferromagnet at finite temperatures with the use of the second-order Green's function theory.The spin wave spectrum, however, does not show exactly wqoc I sin ql at finite temperatures.
A Wigner-Jordan (WJ) transformation is used to study the one-dimensional (1D) and two-dimensional (2D) quantum antiferromagnetic Heisenberg model. The advantage of using the Wigner-Jordan transformation is that it preserves all spin-commutation relations as well as the spin on-site exclusion principle. In the 1D case a nearest-neighbor covalent-bonding state of the WJ fermions is found to have a ground-state energy (-0.4351J per site) comparable with that from the Bethe-ansatz solution (-0.4431J per site), and a linear energy spectrum at low energies with velocity 1.6366J, in close agreement with the velocity obtained by Haldane for the quantum antiferromagnetic Heisenberg model with 1/
d2 interaction (1.5708J). The method used for studying the 1D model is then applied to the 2D Heisenberg model in a square lattice. The resulting state at finite temperature is the in-phase flux state, i.e., a flux state of the Wigner-Jordan spinless fermions with an in-phase fermion orbital current circulating around each elementary plaquette.The single-particle excitation spectrum, i.e., the energy dispersion of reversing orientation of a spin in the system, of the in-phase flux state is overall similar to that of spin waves, with significant difference near the edge point k=(\ensuremath{\pi},0), at which the excitation energy of the WJ fermion is zero, whereas that of the spin-wave excitation is 2J. The specific heat of the in-phase flux state predicts a correct temperature dependence over the entire temperature range, namely a
T2 dependence at low temperature, a peak near T/J=0.6, and a 1/
T2 decreasing at high temperature. It also gives excellent agreement with the specific heat calculated from numerical methods. In contrast, the spin-wave theory only correctly predicts a
T2 dependence at low temperature. The Raman spectrum of the in-phase flux state is calculated and shows significant improvement over that from spin-wave theories compared with the experimental spectrum of
La2CuO4. The exchange parameter, J, obtained from the comparison is 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in agreement with that obtained from analyzing the neutron-scattering data.
In terms of spinless fermions via the Jordan-Wigner transformation along a snake-like path and spin waves modified so as to restore the sublattice symmetry, we investigate static and dynamic properties of two-leg antiferromagnetic Heisenberg ladders. The specific heat is finely reproduced by the spinless fermions, whereas the magnetic susceptibility is well described by the modified spin waves. The nuclear spin-lattice relaxation rate is discussed in detail with particular emphasis on its novel field dependence.