Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization

TL;DR

This paper explores a spin-orbital model on a triangular lattice, revealing a resonating valence-bond liquid phase characterized by entangled spin and orbital states, with quantum fluctuations playing a key role.

Contribution

It provides evidence for a resonating spin-orbital liquid phase in a frustrated triangular lattice model using exact diagonalization, highlighting the importance of quantum fluctuations.

Findings

Identification of a disordered spin-orbital liquid phase.

Presence of entangled states on bonds in the liquid phase.

Smooth crossovers between different regimes in the thermodynamic limit.

Abstract

We investigate the ground state of the $d^1$ spin-orbital model for triply degenerate $t_{2g}$ orbitals on a triangular lattice which 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 which interpolates between the 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 which coexist with supporting them dimer orbital correlations. Such local configurations contribute to the disordered ground states found for the clusters with periodic boundary conditions which 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.