The dynamic conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of strongly correlated electrons in a symmetry-broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry-broken phase is the charge density wave (CDW) with wave vector Q=(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi}${)}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e., an expansion in the inverse dimension 1/d is used. The finite dimensionality is accounted for by the inclusion of linear terms in 1/d and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the nonsymmetry-broken and in the symmetry-broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit T\ensuremath{\rightarrow}0 due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity \ensuremath{\sigma}(\ensuremath{\omega}) the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order 1/d lead to an excitonic resonance lying within the gap. \textcopyright{} 1996 The American Physical Society.
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 .
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.
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.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
The Holstein model of spinless fermions interacting with dispersionless phonons in one dimension is studied by a Green's function Monte Carlo technique. The ground-state energy, first fermionic excited state, density wave correlations, and mean lattice displacements are calculated for lattices of up to 16 sites, for one fermion per two sites, i.e., a half-filled band. Results are obtained for values of the fermion hopping parameter of t=0.1\ensuremath{\omega}, \ensuremath{\omega}, and 10\ensuremath{\omega}, where \ensuremath{\omega} is the phonon frequency. At a finite fermion-phonon coupling g there is a transition from a metallic phase to an insulating phase in which there is charge-density-wave order. Finite-size scaling is found to hold in the metallic phase and is used to extract the coupling dependence of the Luttinger liquid parameters, ${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$ and ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, the velocity of charge excitations, and the correlation exponent, respectively. For free fermions (g=0) and for strong coupling (
g2\ensuremath{\gg}t\ensuremath{\omega}) our results agree well with known analytic results. \textcopyright{} 1996 The American Physical Society.