The excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N\'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.
We present low-temperature static and dynamic properties of the quantum one-dimensional isotropic integer spin Heisenberg magnet with antiferromagnetic nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions. The modified spin-wave theory is used to provide quantities such as the spin-wave dispersion relation, the ground-state energy, the gap and its dependence with temperature, and the asymptotic behaviour of the spin–spin correlation function. The ground state energy and the singlet–triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. Our results show that the ground-state and the gap energies increase with j, in accordance with numerical results available in the literature. The calculation of the dynamic correlation function is performed using the projection operator formalism: the procedure includes up to two-magnon processes. We show that, depending on the values of the frustration parameter j, the wavevector and the temperature, a double-peak structure for the dynamical correlation function can develop.
We investigate full dynamical behaviors of the spin-Peierls transition in
S=1/2 Heisenberg antiferromagnetic chains by means of two-time Green's functions. The effect of temperature-dependent lattice displacements is incorporated self-consistently. Depending on temperature T and transfer wave number k, the imaginary part of the dynamical susceptibility ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ shows rich structures: At
T=0, it is nonvanishing in the frequency region ${\ensuremath{\Omega}}_{M}(k)<\ensuremath{\Omega} (\ensuremath{\equiv}\ensuremath{\Elzxh}\ensuremath{\omega}/J)<{\ensuremath{\Omega}}_{H}(k).$ ${\ensuremath{\Omega}}_{M}(k)$ denotes a lower edge of a triplet magnetic excitation continuum, and is finite at
k=0 due to lattice distortion. The upper edge ${\ensuremath{\Omega}}_{H}(k)$ increases as
k=0 is approached, which is completely different from the feature without lattice distortion. An asymmetric line shape of ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ is found with a peak at the frequency slightly higher than ${\ensuremath{\Omega}}_{M}(k).$ At
0<T<TSP (spin-Peierls transition point) there appears another structure due to thermal fluctuations in the lower-frequency region, $0<\ensuremath{\Omega}<{\ensuremath{\Omega}}_{L}(k).$ Since ${\ensuremath{\Omega}}_{L}(k)<{\ensuremath{\Omega}}_{M}(k),$ the forbidden band always exists at
T<TSP. Above
TSP, ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ reduces to a smooth curve characterized by a single broad maximum. These features in dynamics are systematically explained in terms of different quasiparticle scattering processes proper to the spin-Peierls phase. The results are compared with recent experimental data of neutron scattering for the inorganic compound
CuGeO3.Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.
We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-
21 antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with
2N spins is ferrimagnetic with the total spin
SG=N∕2 for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin
S=SG+1 sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin
S=SG+1 is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.
We calculate the dynamical structure factors of the magnetization plateau state in the
S=21 bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.