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arXiv:1103.1967 · Journal of Statistical Mechanics Theory and Experiment

Phase diagram of theXXZferrimagnetic spin-(1/2, 1) chain in the presence of transverse magnetic field

A. Langari, J Abouie, M Z Asadzadeh, M Rezai

Published Aug 8, 2011• 6 citations

Abstract

We investigate the phase diagram of an anisotropic ferrimagnetic spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U (1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the Néel phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase transitions. The spin-flop phase corresponds to the spontaneous breaking of Z 2 symmetry. We use the numerical density matrix renormalization group and analytic spin wave theory to find the phase diagram of the model. The energy gap, sublattice magnetization and total magnetization parallel and perpendicular to the magnetic field are also calculated. The elementary excitation spectra are obtained via the spin wave theory in the three different regimes depending on the strength of the magnetic field.

DOI: 10.1088/1742-5468/2011/08/p08001

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We investigate the phase diagram of an anisotropic ferrimagnetic spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U (1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the Néel phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase transitions. The spin-flop phase corresponds to the spontaneous breaking of Z 2 symmetry. We use the numerical density matrix renormalization group and analytic spin wave theory to find the phase diagram of the model. The energy gap, sublattice magnetization and total magnetization parallel and perpendicular to the magnetic field are also calculated. The elementary excitation spectra are obtained via the spin wave theory in the three different regimes depending on the strength of the magnetic field.

The spin-1/2 quantum anisotropic

\mathrm{XY}

spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.

The spin-1/2 quantum anisotropic XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.

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 magnetization curve of the

(S,s)=(1,1/2)

ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for

D=0.

Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between

D<{D}_{c}

and

D>{D}_{c}.

The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.

We have studied the zero-temperature phase diagram of

\mathrm{XYZ}

model in the presence of transverse magnetic field. We show that small anisotropy $(0<~\ensuremath{\Delta}<1)$ is not relevant to change the universality class. The phase diagram consists of two antiferromagnetic ordering and a paramagnetic phase. We have obtained the critical exponents, fixed points, and running of coupling constants by implementing the standard quantum renormalization group. The continuous phase transition from antiferromagnetic (spin-flop) phase to a paramagnetic one is in the universality class of Ising model in transverse field. Numerical exact diagonalization has been done to justify our results. We have also addressed the application of our findings to the recent experiments on

{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.