We examine the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and the chemical potential $\ensuremath{\mu}$, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of $\ensuremath{\mu}$ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that $\ensuremath{\sigma}(\ensuremath{\omega})$ shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.
High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory and its cluster extensions, as well as the finite-temperature Lanczos method to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattices at half-filling and at 15% hole doping. We find that for $T\ensuremath{\gtrsim}1.5t$ the self-energy becomes practically local, while the finite-size effects become small at lattice size $4\ifmmode\times\else\texttimes\fi{}4$ for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.
The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ sites. Spectral-weight distributions at half-filling and their doping dependence in the 20-site cluster are found to be similar to those in a $\sqrt{18}\ifmmode\times\else\texttimes\fi{}\sqrt{18}$ cluster, but different from $4\ifmmode\times\else\texttimes\fi{}4$ results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.
The spectral weight functions and the optical conductivity of a highly correlated electronic system described by a simple Hubbard model are studied. The calculations are carried out for a small system, a cubic cluster of eight sites, by means of exact diagonalization using symmetrized basis functions. The spectral weight functions of a single hole (or electron) placed in an otherwise half-filled band are obtained. The density of states at different interaction strengths, ranging from weak to strong couplings, is studied. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. The nature of band narrowing is also discussed. The frequency dependent (optical) conductivity is studied for the cases of a half-filled band, and for one hole and two hole dopings away from half filling. The interaction strength is varied between the weak- and strong-coupling limits. The formation of a Hubbard gap is observed. Results are related to aspects of the metal-insulator transition in bulk systems.
We investigate the extended t-J model (which may include a small next-nearest-neighbor antiferromagnetic coupling or a small hole-hole nearest-neighbor repulsion) by exact-diagonalization techniques. The calculation is done for one and two holes on a 4\ifmmode\times\else\texttimes\fi{}4 torus with arbitrary twisted boundary conditions. The role of the boundary conditions on the ground-state energy, the band width, the charge stiffness, and the optical conductivity is extensively studied. In the two-dimensional space of the twist angles (to be viewed as fluxes through the holes of the torus) the ground-state energy surface exhibits multiple level crossings and may present, locally, a negative curvature (or stiffness) characteristic of a paramagnetic behavior. For two holes and sufficiently large J/t (J/t>0.7) the minima of the energy surface in the parameter space of the fluxes are separated by half a flux quantum. The optical conductivity is calculated by averaging over the boundary conditions in order to minimize finite-size effects and to converge more rapidly toward the thermodynamic limit. We find three different contributions to the optical conductivity; (i) a Drude peak at \ensuremath{\omega}=0, (ii) a broad absorption band in the range J2t, and (iii) a tail extending to larger frequencies (2t7t) associated to the diffusive character of the hole states at these energies.Typically, at low doping density (6%) for a wide range of J/t, and at intermediate doping (12%) for small J/t, these three components account for roughly 30%, 50%, and 20% of the total spectral weight, respectively. At small ratio J/t, both Drude weight and finite-frequency absorption scale almost proportionally with the doping density. However, with increasing J/t, the effective hole-hole attraction (for 12% doping) leads to a transfer of weight from finite frequency to zero frequency. In contrast to the quasiparticle mass, in the J/t\ensuremath{\rightarrow}0 limit, the optical mass defined through the weight of the Drude \ensuremath{\delta}-function peak does not increase like \ensuremath{\sim}t/J but, rather, approaches a limit around \ensuremath{\sim}5. We discuss our results in connection with the optical experiments in the high-
Tc cuprates and suggest that the observed mid-infrared band is due to the strong coupling between the mobile holes and the spin excitations of the Mott insulator, as expected from a description in terms of the t-J Hamiltonian.
The single-particle Green's function for the strong-coupling limit of the single-band Hubbard model ( t-J model) at half-filling is calculated numerically using a Lanczos algorithm. Two-dimensional systems of up to 18 sites with periodic boundary conditions are examined, and evidence is presented for a coherent quasi-particle band of width J which emerges at the low-energy edge of the incoherent spectrum. We find the quasi-particle dispersion to be consistent with ε k = ( J /2)[cos ( k x ) + cos ( k y )] 2 , corresponding to effective next-nearest-neighbour hopping.