Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model

TL;DR

Using tensor-network algorithms, we studied a spin-orbital model on a triangular lattice, finding a stripe order instead of the previously conjectured spin-orbital liquid, highlighting the role of quantum fluctuations in such systems.

Contribution

This work provides the first tensor-network study of the SU(2)×SU(2)×U(1) spin-orbital model, revealing symmetry breaking and stripe order contrary to earlier conjectures.

Findings

The two SU(2) symmetries are broken, leading to stripe order.

The stripe order magnitude is about half that of the spin-1/2 triangular Heisenberg antiferromagnet.

Spin-orbital liquid state is absent in this model.

Abstract

By using the tensor-network state algorithm, we study a spin-orbital model with SU(2)$\times$SU(2)$\times$U(1) symmetry on the triangular lattice. This model was proposed to describe some triangular $d^1$ materials and was argued to host a spin-orbital liquid ground state. In our work the trial wavefunction of its ground state is approximated by an infinite projected entangled simplex state and optimized by the imaginary-time evolution. Contrary to the previous conjecture, we find that the two SU(2) symmetries are broken, resulting in a stripe spin-orbital order with the same magnitude $m=0.085(10)$. This value is about half of that in the spin-1/2 triangular Heisenberg antiferromagnet. Our result demonstrates that although the long-sought spin-orbital liquid is absent in this model the spin-orbital order is significantly reduced due to the enhanced quantum fluctuation. This suggests that high-symmetry spin-orbital models are promising in searching for exotic states of matter in condensed-matter physics.