Abstract The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, 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 UIPL = 0.572 < UIPH = 1.914 < UIP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below UIP/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 findings for the phase scenario of the Hubbard model is shown.
The phase diagram of spinless fermions with repulsive interaction on a hypercubic lattice is calculated analytically in infinite dimensions. For 0T0.183 the susceptibility \ensuremath{\chi}(k) diverges for incommensurate values of k thus masking a region of phase separation including a tricritical point. In this region a new phase must exist. Its structure is still unknown in spite of the simplicity of the model. We compare our finding to results for other interacting fermion systems and discuss its possible relation to superconductivity.
We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in a homogeneous
p+ip superconducting (SC) phase at high or low fermion densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain
p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above
Tsc, generating a homogeneous normal phase (far away from
n=1/2), or a PS between normal phases with different densities (close to
n=1/2). Further increasing temperature to
Tps, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on the filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/particle doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite
V and extends to finite doping regime.
Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional Φ in powers of the inverse lattice dimension 1/d. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in d = 3. The Bethe-Salpeter equation is evaluated for the conductivity σ(ω) which is found to have two peaks within the energy gap 2∆ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, σ DC does not vanish for T → 0 1 The limit of infinite dimensions d → ∞ for itinerant fermion systems [1, 2] has proven very useful for the understanding of strongly interacting electron systems [3]. The research focusses on one-particle properties in the strict limit d = ∞. There exist also some results on transport properties [4, 5]. The present contribution extends the knowledge on the AC- and DC-conductivity including 1/d-corrections in the model of spinless fermions with repulsive interaction. The results cover and the non-symmetry broken (homogeneous) phase and the AB-CDW occurring on bipartite lattices. The techniques used in the description of the latter are certainly transferable to other symmetry broken phases in related models. The Hamiltonian of the spinless fermion model at half-filling (n = 0.5) is given in second quantisation
An analytic expression for the dynamical conductivity sigma ( omega ) of spinless fermions with local disorder and nearest-neighbour repulsion is derived on lattices with infinite coordination number Z. The model is exactly solvable in the whole parameter range assuming two possible phases: a homogeneous phase and a checkerboard charge-density wave (CDW). Away from half filling the system displays anomalous behaviour: weak particle-density fluctuations favour spontaneous symmetry breaking. First, the authors investigate the effects of this anomaly on the conductivity in the AC and DC regimes. Second, they focus on the Mott transition occurring at zero temperature at half filling. The critical exponents for the conductivity are computed for the dependence on the interaction U, the disorder gamma , the filling n, the temperature T and the frequency omega .
The spinless Falicov-Kimball model is solved exactly in the limit of infinite dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large
U, and charge-density-wave order, which is prevalent at moderate
U, is examined in detail. We find a rich phase diagram that displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when
U is large enough to generate a correlation-induced gap in the single-particle density of states.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (
t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For
t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero
t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of
t∣IH.