The many-electron ground state of the adiabatic Holstein model in two and three dimensionsB. Poornachandra Sekhar, Sanjeev Kumar and Pinaki Majumdar
Harish-Chandra Research Institute - Chhatnag Road, Jhusi, Allahabad 211 019, India
received 7 June 2004; accepted in final form 15 September 2004
published online 9 October 2004
We present the complete ground-state phase diagram of the Holstein model in two and three dimension considering the phonon variables to be classical. We first establish the overall structure of the phase diagram by using exact-diagonalisation-based Monte Carlo (ED-MC) on small lattices and then use a new "travelling cluster" approximation (TCA) for annealing the phonon degrees of freedom on large lattices. The phases that emerge include a Fermi liquid (FL), with no lattice distortions, an insulating polaron liquid (PL) at strong coupling, and a charge-ordered insulating (COI) phase around half-filling. The COI phase is separated from the Fermi liquid by a regime of phase coexistence whose width grows with increasing electron-phonon coupling. We provide results on the electronic density of states, the COI order parameter, and the spatial organisation of polaronic states, for arbitrary density and electron-phonon coupling. The results highlight the crucial role of spatial correlations in this strong-coupling problem.
71.38.-k - Polarons and electron-phonon interactions.
71.45.Lr - Charge-density-wave systems.
71.10.Fd - Lattice fermion models (Hubbard model, etc.).
© EDP Sciences 2004