The SU(4) Heisenberg model can serve as a low-energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric or in systems of alkaline-earth atoms on an optical lattice. Recently, it has been argued that on the honeycomb lattice, the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward the spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave function of fermions with $\ensuremath{\pi}$-flux state, we find that the algebraic liquid is robust and that a small finite value of the next-nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest-neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette-product state is an exact ground state.
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the
eg Mott insulator
Ba3CuSb2O9 and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.
Dirac spin liquids represent a class of highly-entangled quantum phases in two dimensional Mott insulators, featuring exotic properties such as critical correlation functions and absence of well-defined low energy quasi-particles. Existing numerical works suggest that the spin-orbital
SU(4) symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice realizes a Dirac spin-orbital liquid, described at low energy by
(2+1)d quantum electrodynamics (QED
3) with
Nf=8 Dirac fermions. We generalize methods previously developed for
SU(2) spin systems to analyze the symmetry properties and stability of the Dirac spin-orbital liquid. We conclude that the standard Dirac state in the
SU(4) honeycomb system, based on a simple parton mean-field ansatz, is intrinsically unstable at low energy due to the existence of a monopole perturbation that is allowed by physical symmetries and relevant under renormalization group flow. We propose two plausible alternative scenarios compatible with existing numerics. In the first scenario, we propose an alternative
U(1) Dirac spin-orbital liquid, which is similar to the standard one except for its monopole symmetry quantum numbers. This alternative
U(1) state represents a stable gapless phase. In the second scenario, we start from the standard
U(1) Dirac liquid and Higgs the
U(1) gauge symmetry down to
Z4. The resulting
Z4 Dirac spin-orbital liquid is stable. We also discuss the continuous quantum phase transitions from the
Z4 Dirac liquids to conventional symmetry-breaking orders, described by the QED
3 theory with
Nf=8 supplemented with a critical charge-
4 Higgs field. We discuss possible ways to distinguish these scenarios in numerics. We also extend previous calculations of the quantum anomalies of QED
3 and match with generalized lattice Lieb-Schultz-Mattis constraints.
Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we study several spin-orbital liquid states, including a uniform $\ensuremath{\pi}$-flux state, three stripy states, and a plaquette state, on the $L\ifmmode\times\else\texttimes\fi{}L$ torus up to
L=24. It turns out that one of these stripy states, called the ``stripe-II'' state, is energetically favored. This ground state breaks the
C6 symmetry of the lattice, resulting in a reduced
C2 symmetry and doubled unit cells while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform $\ensuremath{\pi}$-flux state.
Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU(4) Kugel-Khomskii (KK) model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we have studied several spin-orbital liquid states, including a uniform
π flux state, three stripy states, and a plaquette state, on the
L×L torus up to
L=24. It turns out that one of these stripy states, called the "stripe-II" state, is energetically favored. This ground state breaks the
C6 symmetry of the lattice, resulting in a reduced
C2 symmetry and doubled unit cells, while preserving the SU(4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform
π-flux state.
We study a spin-orbital model for
4d1 or
5d1 Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudo-orbital operators representing multipoles of the effective
j=23 angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate
Ba2YMoO6. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic x-ray scattering (RIXS) amplitudes for double-perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions.