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arXiv:cond-mat/0310223 · Physical Review B

Quantum phase transitions in the one-dimensional S=1 spin-orbital model: Implications for cubic vanadates

Satoshi Miyashita, Akira Kawaguchi, Norio Kawakami, Giniyat Khaliullin

Published Mar 24, 2004• 11 citations
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Abstract

We investigate ground-state properties and quantum phase transitions in the one-dimensional $S=1$ spin-orbital model relevant to cubic vanadates. Using the density-matrix renormalization group, we compute the ground-state energy, the magnetization, and the correlation functions for different values of the Hund's coupling ${J}_{H}$ and the external magnetic field. It is found that the magnetization jumps at a certain critical field, which is a hallmark of the field-induced first-order phase transition. The phase transition driven by ${J}_{H}$ is also of first order. We also consider how the lattice-induced ferro-type interaction between orbitals modifies the phase diagram, and discuss the results in a context of the first-order phase transition observed in ${\mathrm{YVO}}_{3}$ at 77 K.

DOI
10.1103/physrevb.69.104425

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We investigate ground-state properties and quantum phase transitions in the one-dimensional S=1S=1S=1 spin-orbital model relevant to cubic vanadates. Using the density-matrix renormalization group, we compute the ground-state energy, the magnetization, and the correlation functions for different values of the Hund's coupling JH{J}_{H}JH​ and the external magnetic field. It is found that the magnetization jumps at a certain critical field, which is a hallmark of the field-induced first-order phase transition. The phase transition driven by JH{J}_{H}JH​ is also of first order. We also consider how the lattice-induced ferro-type interaction between orbitals modifies the phase diagram, and discuss the results in a context of the first-order phase transition observed in YVO3{\mathrm{YVO}}_{3}YVO3​ at 77 K.
We study quantum phase transitions induced by the on-site spin-orbit interaction $\ensuremath{\lambda}\mathbf{L}\ensuremath{\cdot}\mathbf{S}$ in a toy model of vanadium chains. In the $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization-group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin N\'eel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds CaV2O4{\text{CaV}}_{2}{\text{O}}_{4}CaV2​O4​ and ZnV2O4{\text{ZnV}}_{2}{\text{O}}_{4}ZnV2​O4​ are also discussed.
We present the zero-temperature phase diagram of the one-dimensional t2g{t}_{2\mathrm{g}}t2g​-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case of the electron density n=5n=5n=5 corresponding to five electrons per site, while several other cases for electron densities between n=3n=3n=3 and 6 are also studied. At n=5n=5n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase, with power-law slowly decaying correlations, and a fully polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the n=5n=5n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states against varying parameters suggests that they may be of relevance in quasi-one-dimensional Co-oxide materials, or even in higher dimensional cobaltite systems as well.
We investigate ground-state properties of a one-dimensional S=1 spin-orbital model with or without uniaxial single-ion anisotropy. By means of the density matrix renormalization group method, we compute the ground-state energy, the magnetization curves and the correlation functions. We discuss how the ground-state properties depend on the two exchange couplings for orbital and spin sectors. The phase diagram obtained is compared with that for the S=1/2 model. We also address the effect of uniaxial single-ion anisotropy.
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We report a quantum phase transition between orbital-selective Mott states, with different localized orbitals, in a Hund's metals model. Using the density matrix renormalization group, the phase diagram is constructed varying the electronic density and Hubbard UUU, at robust Hund's coupling. We demonstrate that this transition is preempted by charge fluctuations and the emergence of free spinless fermions, as opposed to the magnetically driven Mott transition. The Luttinger correlation exponent is shown to have a universal value in the strong-coupling phase, whereas it is interaction dependent at intermediate couplings. At weak coupling we find a second transition from a normal metal to the intermediate-coupling phase.
We study a version of the one-dimensional spin-orbital model with spins S=1S=1S=1 relevant to cubic vanadates. At small Hund's coupling JH{J}_{H}JH​ we discover dimerization in a pure electronic system solely due to a dynamical spin-orbital coupling. Above a critical value JH,{J}_{H},JH​, a uniform ferromagnetic state is stabilized at zero temperature. More surprisingly, we observe a temperature driven dimerization of the ferrochain, which occurs due to a large entropy released by dimer states. This dynamical dimerization seems to be the mechanism driving the peculiar intermediate phase of YVO3.{\mathrm{YVO}}_{3}.YVO3​.