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arXiv:cond-mat/0212368 · Physical review. B, Condensed matter

Entropy driven dimerization in a one-dimensional spin-orbital model

Jesko Sirker, Giniyat Khaliullin

Published Mar 28, 2003• 41 citations
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Abstract

We study a version of the one-dimensional spin-orbital model with spins $S=1$ relevant to cubic vanadates. At small Hund's coupling ${J}_{H}$ we discover dimerization in a pure electronic system solely due to a dynamical spin-orbital coupling. Above a critical value ${J}_{H},$ 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 ${\mathrm{YVO}}_{3}.$

DOI
10.1103/physrevb.67.100408

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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​.
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 the effects of hole doping on one-dimensional Mott insulators with orbital degrees of freedom. We describe the system in terms of a generalized $t\text{\ensuremath{-}}J$ model. At a specific point in parameter space the model becomes integrable in analogy to the one-band supersymmetric $t\text{\ensuremath{-}}J$ model. We use the Bethe ansatz to derive a set of nonlinear integral equations which allow us to study the thermodynamics exactly. Moving away from this special point in parameter space we use the density-matrix renormalization group applied to transfer matrices to study the evolution of various phases of the undoped system with doping and temperature. Finally, we study a one-dimensional version of a realistic model for cubic titanates which includes the anisotropy of the orbital sector due to Hund's coupling. We find a transition from a phase with antiferromagnetically correlated spins to a phase where the spins are fully ferromagnetically polarized, a strong tendency toward phase separation at large Hund's coupling, as well as the possibility of instability toward triplet superconductivity.
The Hund's coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean-field theory, we explore the effect of local moment formation, spin, and charge excitations on the entropy and specific heat of the three-orbital model. For fillings $2\ensuremath{\lesssim}n<3$ and low temperature, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase to values comparable to the half-filled Mott insulator. We also discuss the appearance of entropy plateaus and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. The temperature scale for charge excitations is almost independent of filling and given by $\ensuremath{\approx}0.2U$, with UUU the intraorbital repulsion. Local spin excitations become relevant for filling n>1n>1n>1 and their characteristic temperature is proportional to the Hund coupling JJJ, with a filling-dependent prefactor. The analysis of the specific heat in the atomic limit yields accurate predictions for these features in the strong-coupling regime.
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{XXZ}$ model with SU(2) spin exchange and anisotropic XXZ\text{XXZ}XXZ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{SU}$(2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
To demonstrate the role played by the von Neumann entropy (vNE) spectra in quantum phase transitions we investigate the one-dimensional anisotropic SU(2) spin–orbital model with negative exchange parameter. In the case of classical Ising orbital interactions we discover an unexpected novel phase with Majumdar–Ghosh-like spin–singlet dimer correlations triggered by spin–orbital entanglement (SOE) and having orbital correlations, while all the other phases are disentangled. For anisotropic XXZ orbital interactions both SOE and spin–dimer correlations extend to the antiferro-spin/alternating-orbital phase. This quantum phase provides a unique example of two coupled order parameters which change the character of the phase transition from first-order to continuous. Hereby we have established the vNE spectral function as a valuable tool to identify the change of ground state degeneracies and of the SOE of elementary excitations in quantum phase transitions.
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.