Phase diagram of Holstein-Kondo lattice model at half-filling
  We study the Kondo lattice model which is modified by the Holstein term, involving both the Kondo exchange coupling and the electron-phonon coupling constants, characterized by $J$ and $g$, respectively. The model is solved by employing the dynamical mean-field theory in conjunction with exact diagonalization technique. A zero temperature phase diagram of symmetry unbroken states at half filling is mapped out which exhibits an interplay between the two interactions and accounts for both spin and charge fluctuations. When the Kondo exchange coupling is dominant the system is in Kondo insulator state. Increasing $g$ for small values of $J$ leads to a Kondo insulator-metal transition. Upon further enhancement of $g$ a transition to the bipolaronic insulating phase takes place. Also a small region with non-Fermi liquid behavior is found near the Kondo insulator-metal transition. 
Reza Nourafkan, Nasser Nafari