Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
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.
A quantum spherical spin model with an antiferromagnetic coupling
J on the
AB2 chain is studied, whose topology is of interest in the context of ferrimagnetic polymers and oxocuprates. A ferrimagnetic long-range order is found at the only critical point
g=T=h=0, where
T denotes the temperature,
h the magnetic field, and
g the quantum coupling constant in energy units. The approach to the critical point, with diverging correlation length $\ensuremath{\xi}$ and cell susceptibility ${\ensuremath{\chi}}_{\text{cell}}$, is characterized through several paths in the
g,T,h parameter space: for $(T∕J)\ensuremath{\rightarrow}0$ and
g=h=0, ${\ensuremath{\chi}}_{\text{cell}}\ensuremath{\sim}1∕{T}^{2}$, as also found in several classical and quantum spherical and Heisenberg models; for $(h∕J)\ensuremath{\rightarrow}0$ and
g=T=0, ${\ensuremath{\chi}}_{\text{cell}}\ensuremath{\sim}1∕h$; and for $(g∕J)\ensuremath{\rightarrow}0$ and
T=h=0, $\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\chi}}_{\text{cell}}\ensuremath{\sim}1∕\sqrt{g}$, thus evidencing an essential singularity due to quantum fluctuations. In any path chosen the relation ${\ensuremath{\chi}}_{\text{cell}}\ensuremath{\sim}{\ensuremath{\xi}}^{2}$ is satisfied. For finite
g and
T a field-induced short-range ferrimagnetism occurs to some extent in the
g,T,h space, as confirmed by the analysis of the local spin averages, cell magnetization with a rapid increase for very low fields, and spin-spin correlation functions. The asymptotic limits of the correlation functions are also provided with respect to
g,
T,
h, and spin distance. The analysis of the entropy and specific heat reveals that the quantum fluctuations fix the well-known drawback of classical spherical models concerning the third law of thermodynamics.