Kai Phillip Schmidt, Lehrstuhl fuer Theoretische Physik I, TU Dortmund
The Hubbard model is one of the most studied microscopic models in condensed matter physics. It
describes on a very simple level the interplay between the kinetics and the Coulomb interaction of
electrons in solid state systems. Generically, one expects at half filling a metallic phase for large
kinetics while a Mott insulator is present for large interactions. In most cases the Mott phase shows
additionally long-range spin order, since the Hubbard model can be mapped to a Heisenberg model
in the strong-coupling limit. A direct transition between the metal and the long-range ordered Mott
insulator was considered to be the standard case for a long time.
But in recent years there are more and more evidences that especially on frustrated lattices there is
the possibility of exotic and insulating intermediate phases without long-range order. It is therefore
an obviously relevant question what kind of effective low-energy theory describes such Mott phases
and how to derive them. This is particular complicated when the spin liquid is located close to the
metal-insulator transition as for the recently discovered spin liquid of the Hubbard model on the
honeycomb lattice. In this talk we discuss these issues for the Mott phase of the Hubbard model on
the triangular and on the honeycomb lattice.
H.Y. Yang, A. Laeuchli, F. Mila, and K.P. Schmidt,
Effective spin model of the spin-liquid phase of the Hubbard model on the triangular lattice
Physical Review Letters 105 , 267204 (2010)
H.Y. Yang and K.P. Schmidt,
Effective models for gapped phases of strongly correlated quantum lattice models
European Physics Letters 94 , 17004 (2011)