Spin-orbital quantum liquid on the honeycomb lattice

TL;DR

This paper provides evidence that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a quantum spin-orbital liquid with algebraic correlations, supported by multiple theoretical and numerical methods.

Contribution

It demonstrates that the honeycomb lattice Kugel-Khomskii model is an algebraic quantum spin-orbital liquid, unifying various approaches and connecting to experimental systems.

Findings

No symmetry breaking observed in the model

Correlations are algebraic due to Dirac points

Model explains spin-orbital liquid behavior in Ba3CuSb2O9

Abstract

In addition to low-energy spin fluctuations, which distinguish them from band insulators, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in most situations spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking - lattice or SU(N) - is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave-function based on the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms.