Theory of electrons with orbital degeneracy
You-Quan Li (Augsburg U./ZIMP Zhejiang U.), U. Eckern (Augsburg U.)
TL;DR
This paper explores the symmetry properties and ground state characteristics of the Hubbard model with orbital degeneracy, revealing underlying SU(4) and SU(4)/charge symmetries, and mapping to effective spin models.
Contribution
It uncovers hidden symmetries in the Hubbard model with orbital degeneracy and establishes mappings to effective spin models at different fillings.
Findings
Strong coupling system maps to SO(6) Heisenberg magnet at half-filling.
System is equivalent to SU(4) magnet at quarter-filling.
Ground state features and low-lying excitations are characterized in one dimension.
Abstract
The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SU_d(4) symmetry of spin-orbital double. A hidden charge SU_c(4) symmetry is exposed and an extended Lieb-Mattis transformation which maps these two symmetries into each other is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6) Heisenberg magnet at half-filling and a SU(4) one at quarter-filling. The band is half-filled at all temperature for . The features of ground state and low-lying excitations in one dimension are indicated according to exact solutions. Various possibilities of symmetry breaking are also given.
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