We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behaviour: at very low temperatures, the specific heat and the magnetic susceptibility multiplied by the temperature behave like and , respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give precise estimates for the low-temperature behaviour.
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.We present results for the dynamic structure factor of the
S=1∕2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\ensuremath{\lambda}\ensuremath{\approx}0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the
S=1 bound state which remains well defined up to temperatures of the order of
J. The variation with temperature and wave vector of the integrated intensity for one-magnon and two-magnon scattering and of the central peak are discussed.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and
1/2, antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.
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.