Abstract
The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, 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 spin-orbital symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking—lattice or —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 -flux state of fermions on the honeycomb lattice at 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 an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of . The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.
- Received 27 July 2012
DOI:https://doi.org/10.1103/PhysRevX.2.041013
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Published by the American Physical Society
Popular Summary
Development of order in physical materials at low temperatures almost seems like a matter of course, as exemplified by the freezing of most liquids into crystals and by a nonmagnetic material turning magnetic as its temperature is lowered. The former involves the collective ordering of molecules in space, and the latter the collective ordering of the microscopic spins carried by the atoms (or their electrons) in the material. Naturally, materials that go against this matter of course excite physicists. A recent experiment on a copper oxide, , has just generated new excitement, in the form of a fundamental search for quantum spin-orbital liquids, where the most important electrons show no signs of collectively ordering their spins and choosing which orbitals to occupy. In this paper, we have investigated a minimal theoretical model and shown the strongest evidence to date for the existence of a spin-orbital-liquid state in the model down to the lowest temperature possible.
The model is a so-called Kugel-Khomskii spin-orbital model set on a honeycomb lattice. Each constituent particle—modeling an electron in a transitional metal oxide—has two spin states (“up” and “down”) and two orbital states that are degenerate in energy. However, the particles that are nearest neighbors to each other can interact and interchange their spin-orbital states via the interactions. The energetic equivalence of the four spin-orbital states and the symmetric form of the interchange gives the model its symmetry. The choice of honeycomb-lattice setting is motivated by the recent experiment on . The strength of our conclusion about the existence of a spin-orbital-liquid state draws from the convergent indications from investigations based on a number of theoretical techniques with different strengths that complement each other. We have also gained insights into the specific nature of the spin-orbital-liquid state.
Our work provides an interesting starting point for further theoretical work on quantum spin-orbital liquids. We also speculate that our results should serve as a stimulus for the field of cold-atom physics, as they suggest a tantalizing route of using optical lattices with honeycomb geometry in the search for quantum liquids in ultracold fermionic atoms with symmetry.
