Abstract
We investigate the ground state of the spin-orbital model for triply degenerate orbitals on a triangular lattice that unifies intrinsic frustration of spin and orbital interactions with geometrical frustration. Using full or Lanczos exact diagonalization of finite clusters, we establish that the ground state of the spin-orbital model that interpolates between superexchange and direct exchange interactions on the bonds is characterized by valence-bond correlations. In the absence of Hund’s exchange the model describes a competition between various possible valence-bond states. By considering the clusters with open boundary conditions we demonstrate that orbital interactions are always frustrated, but this frustration is removed by pronounced spin singlet correlations that coexist with dimer orbital correlations supporting them. Such local configurations contribute to the disordered ground states found for the clusters with periodic boundary conditions that interpolate between a highly resonating, dimer-based, entangled spin-orbital liquid phase and a valence-bond state with completely static spin-singlet states. We argue that these states are also realized for the infinite lattice and anticipate that pronounced transitions between different regimes found for particular geometries will turn out to smooth crossovers in the properties of the spin-orbital liquid in the thermodynamic limit. Finally, we provide evidence that the resonating spin-orbital liquid phase involves entangled states on the bonds. In such a phase classical considerations based on the mean-field theory cannot be used, spin exchange interactions do not determine spin bond correlations, and quantum fluctuations play a crucial role in the ground states and magnetic transitions.
8 More- Received 16 December 2010
DOI:https://doi.org/10.1103/PhysRevB.83.094406
©2011 American Physical Society