PIRSA:13050045 Conference Quantum Information Condensed Matter

DOI10.48660/13050045

Conference/School: Emergence & Entanglement II 2013

Corboz, P. (2013). Spin-orbital quantum liquid on the honeycomb lattice. Perimeter Institute. https://pirsa.org/13050045

Corboz, Philippe. Spin-orbital quantum liquid on the honeycomb lattice. Perimeter Institute, May. 09, 2013, https://pirsa.org/13050045 

@misc{ pirsa_PIRSA:13050045,
  doi = {10.48660/13050045},
  url = {https://pirsa.org/13050045},
  author = {Corboz, Philippe},
  keywords = {Quantum Information, Condensed Matter},
  language = {en},
  title = {Spin-orbital quantum liquid on the honeycomb lattice},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {may},
  note = {PIRSA:13050045 see, \url{https://pirsa.org}}
}

Abstract

The symmetric Kugel-Khomskii can be seen as a minimal model describing the interactions between spin and orbital degrees of freedom in certain transition-metal oxides with orbital degeneracy, and it is equivalent to the SU(4) Heisenberg model of four-color fermionic atoms. We present simulation results for this model on various two-dimensional lattices obtained with infinite projected-entangled pair states (iPEPS), an efficient variational tensor-network ansatz for two dimensional wave functions in the thermodynamic limit. We find a rich variety of exotic phases: while on the square and checkerboard lattices the ground state exhibits dimer-N\'eel order and plaquette order, respectively, quantum fluctuations on the honeycomb lattice destroy any order, giving rise to a spin-orbital liquid. Our results are supported from flavor-wave theory and exact diagonalization. Furthermore, the properties of the spin-orbital liquid state on the honeycomb lattice are 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 ground state is an algebraic spin-orbital liquid. This model provides a possible 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.

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