Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

Abstract

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in in nite dimensions (d ! 1). In spite of its simplicity the model displays a rich phase diagram depending on the doping , the interaction U and the temperature T . The system can be in the homogeneous phase (hom), the nonsegregated AB charge density wave (ab-cdw), the AB phase separation region (ps-ab/hom; coexistence of ab-cdw and hom), the incommensurate phase (ip) or the IP phase separation region (ps-ab/ip; coexistence of ab-cdw and ip). We identify three important values of the interaction U IPL = 0:572 < U IPH = 1:914 < U IP=PS = 4:212 which distinguish four intervals of U . These imply four di erent types of phase diagrams. In all the three phase diagrams with U below U IP=PS the ip appears. We propose a new general ansatz for the order parameter of this phase. A competition between the ip, the ps-ab/ip and the ps-ab/hom is found. The relevance of our ndings for the phase scenario of the Hubbard model is shown.

Doping-driven metal-insulator transitions and charge orderings in the extended Hubbard model

“…For U = 0 (W > 0) the model (2) is solved using a standard broken-symmetry Hartree-Fock approximation. The mean-field Hamiltonian is diagonalized by means of a Bogoliubov transformation 30,33,[62][63][64][65][66][67][68] . The resulting selfconsistent equations for the total occupation n and the charge polarization ∆ = 1 2 (n A −n B ) are:…”

Exact Single Spin Flip for the Hubbard Model ind=∞

“…The effective one-site problem remains generally difficult to solve [6]. So far, the metal-insulator transition [6] and various ordering phenomena [8][9][10][11][12] have been treated successfully. Recently, the investigation of polarized situations has been started [13,14].…”

Conductivity in a symmetry-broken phase: Spinless fermions with 1/dcorrections

“…Then the truncation of this series yields an approximation to the corresponding order. The power counting for the diagrams of Φ has been explained previously 6,15 . Here it shall just be stated that the first diagram in fig Note that the Fock diagram is seemingly of another order, namely O(1/Z 3/2 ), than the third diagram, O(1/Z), which is called the local correlation diagram henceforth.…”