The magnetic susceptibility and specific heat of the one-dimensional S = 1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of LiVGe2O6 measured by Millet et al. [Phys. Rev. Lett. 83, 4176 (1999)], we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e., with a positive coupling constant.The magnetic susceptibility and specific heat of the one-dimensional S = 1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of LiVGe2O6 measured by Millet et al. [Phys. Rev. Lett. 83, 4176 (1999)], we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e., with a positive coupling constant.

arXiv:cond-mat/0003102Physical Review LettersSep 11, 200043 citations

On biquadratic exchange interactions in spin-1 systems

H. H. Chen

Physics Letters ADec 1, 19741 citation

Algebraic approach to the solution of a one-dimensional model of N interacting particles

A. M. Perelomov

Theoretical and Mathematical PhysicsMar 1, 197155 citations

Magnetic behavior of a spin-1 Blume-Emery-Griffiths model

Francesco Paolo Mancini

I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.

arXiv:0909.5433Journal of Physics Conference SeriesJan 1, 20105 citations

Effective one-dimensional models from matrix product states

Frederik Keim, Götz Silvester Uhrig

arXiv:1503.02616The European Physical Journal BJun 1, 20154 citations

Models with exact ground states connecting smoothly the S= 12 dimer and S=1 Haldane phases of one-dimensional spin chains

Alexei K. Kolezhuk, H.-J. Mikeska

We investigate the isotropic two-leg $S=$ $\frac{1}{2}$ ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians that have a matrix-product wave function as an exact ground state. We demonstrate that a smooth change of parameters leads one from the $S=$ $\frac{1}{2}$ dimer and Majumdar-Ghosh chains to the $S=1$ chain with biquadratic exchange, which proves that these model systems are in the same phase. The family of Hamiltonians also includes a set of models of isotropic $S=$ $\frac{1}{2}$ chains with only bilinear nearest- and next-nearest-neighbor interactions. The ground state for these models becomes unstable at a line of first-order phase transitions to the ferromagnetic state.We investigate the isotropic two-leg $S=$$\frac{1}{2}$ ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians that have a matrix-product wave function as an exact ground state. We demonstrate that a smooth change of parameters leads one from the $S=$$\frac{1}{2}$ dimer and Majumdar-Ghosh chains to the $S=1$ chain with biquadratic exchange, which proves that these model systems are in the same phase. The family of Hamiltonians also includes a set of models of isotropic $S=$$\frac{1}{2}$ chains with only bilinear nearest- and next-nearest-neighbor interactions. The ground state for these models becomes unstable at a line of first-order phase transitions to the ferromagnetic state.

arXiv:cond-mat/9701089Physical review. B, Condensed matterNov 1, 199738 citations

We investigate the isotropic two-leg

S=

\frac{1}{2}

ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians that have a matrix-product wave function as an exact ground state. We demonstrate that a smooth change of parameters leads one from the

S=

\frac{1}{2}

dimer and Majumdar-Ghosh chains to the

S=1

chain with biquadratic exchange, which proves that these model systems are in the same phase. The family of Hamiltonians also includes a set of models of isotropic

S=

\frac{1}{2}

chains with only bilinear nearest- and next-nearest-neighbor interactions. The ground state for these models becomes unstable at a line of first-order phase transitions to the ferromagnetic state.