Hidden symmetries and their consequences in t_{2g} cubic perovskites
Abstract
The fiveband Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystalfield splitting is large, one may consider excitations confined to the lowest threefolddegenerate t_{2g} orbital states. When the electron hopping matrix element (t) is much smaller than the onsite Coulomb interaction energy (U), the Hubbard model can be mapped onto the wellknown effective Hamiltonian (at order t^{2}/U) derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support longrange spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying threeband Hubbard model. Using these symmetries we develop a rigorous MerminWagner construction, which shows that the threeband Hubbard model does not support spontaneous longrange spin order at any nonzero temperature and at any order in t/U—despite the threedimensional lattice structure. The introduction of spinorbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we show that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.
 Publication:

Physical Review B
 Pub Date:
 January 2004
 DOI:
 10.1103/PhysRevB.69.035107
 arXiv:
 arXiv:condmat/0307515
 Bibcode:
 2004PhRvB..69c5107H
 Keywords:

 71.27.+a;
 75.10.b;
 75.30.Et;
 75.30.Gw;
 Strongly correlated electron systems;
 heavy fermions;
 General theory and models of magnetic ordering;
 Exchange and superexchange interactions;
 Magnetic anisotropy;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Materials Science
 EPrint:
 26 pages, 3 figures, 520 KB, submitted Phys. Rev. B