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arXiv:cond-mat/0301533 · Physical review. B, Condensed matter

Spin-orbital gapped phase with least symmetry breaking in the one-dimensional symmetrically coupled spin-orbital model

Guang-Ming Zhang, Hui Hu, Lu Yu

Published Feb 27, 2003• 5 citations
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Abstract

To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean-field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4)-symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreases from large to small values.

DOI
10.1103/physrevb.67.064420

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To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean-field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4)-symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreases from large to small values.
The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J_1/J_2=1/3.
We numerically study the SU(2)⊗\otimes⊗SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum q=πq=πq=π form massless continua which split from the excitations belonging to the [22][2^2][22] irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around q=π/2q=π/2q=π/2 originating from [21122^11^22112] become critical, too.
A generalized one-dimensional $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ spin-orbital model is studied by means of Schwinger boson mean-field theory (SBMFT). We focus on exploring the dimer phases and clarify how to capture properly the low-temperature properties of the system. The phase diagrams for the cases of S=T=1∕2S=T=1∕2S=T=1∕2 and of S=1S=1S=1 and T=1∕2T=1∕2T=1∕2 are presented. Three dimer phases, the orbital valence bond state, spin valence bond state and spin-orbital valence bond state, are found to arise in proper parameter regions. The results indicate that the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ type of spin-orbit coupling can serve as both the spin-Peierls and orbital-Peierls mechanisms which are responsible for the formations of spin singlet and orbital singlet, respectively. We have also calculated the static spin and pseudospin susceptibilities in the SBMFT scheme to characterize and distinguish the three types of dimer phases.
The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless region with algebraically decaying correlation functions $\ensuremath{\sim}\mathrm{cos}[(\ensuremath{\pi}{/2a}_{0})x]{x}^{\ensuremath{-}3/2}$. When entering the massive phase, the system displays an approximate SO(6) enlarged symmetry with a dimerization type of ordering consisting in alternating spin and orbital singlets.
Based on the generalized valence bond picture, a Schwinger boson mean-field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ and $(\ensuremath{\pi}/3,\ensuremath{\pi}/3),$ respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors; the Bose condensation arises at twice this value. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.
The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless region with algebraically decaying correlation functions, ∼cos⁡(π/2a0x)x−3/2\sim \cos(π/{2a_0} x) x^{-3/2}∼cos(π/2a0​x)x−3/2. When entering the massive phase, the system displays an approximate SO(6) enlarged symmetry with a dimerization type of ordering consisting in alternating spin and orbital singlets.