Temperature and Dimensionality Dependences of Optical Absorption Spectra in Mott Insulators

We investigate the temperature dependence of optical absorption spectra of one-dimensional (1D) and two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filed Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that in 1D the energy position of the absorption edge is almost independent of temperature, while in 2D the edge position shifts to lower energy with increasing temperature. The different temperature dependence between 1D and 2D is attributed to the difference of the coupling of the charge and spin degrees of freedom. The implications of the results on experiments are discussed in terms of the dimensionality dependence.Comment: 5 pages, 4 figure

Equivalence of Gutzwiller and slave-boson mean-field theories for multi-band Hubbard models

We demonstrate that a recently introduced slave-boson mean-field theory is equivalent to our Gutzwiller theory for multi-band Hubbard models with general onsite interactions. We relate the different objects that appear in both approaches at zero temperature and discuss the limitations of both methods.Comment: 4 page

Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal-insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott-Hubbard transition in the limit of infinite dimensions.Comment: 15 pages, 3 figure

Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model

For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.Comment: 32 pages, 12 figures, submtted to JSTA

Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional $1/r$-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for half-filled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the~$1/r$-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type wave functions yield reliable predictions on zero temperature phase transitions in low-dimensional, i.e., charge-spin separated systems.Comment: 23 pages + 3 figures available on request; LaTeX under REVTeX 3.

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $L\leq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{\rm c}\approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.Comment: 10 pages, 11 figure

Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping

We discuss the transition from a metal to charge or spin insulating phases characterized by the opening of a gap in the charge or spin excitation spectra, respectively. These transitions are addressed within the context of two exactly solvable Hubbard and tJ chains with long range, $1/r$ hopping. We discuss the specific heat, compressibility, and magnetic susceptibility of these models as a function of temperature, band filling, and interaction strength. We then use conformal field theory techniques to extract ground state correlation functions. Finally, by employing the $g$-ology analysis we show that the charge insulator transition is accompanied by an infinite discontinuity in the Drude weight of the electrical conductivity. While the magnetic properties of these models reflect the genuine features of strongly correlated electron systems, the charge transport properties, especially near the Mott-Hubbard transition, display a non-generic behavior.Comment: 47 pages, REVTEX 3.0, 14 postscript figures available form [email protected] (submitted using the figures-command

The Anderson impurity model with a narrow-band host: from orbital physics to the Kondo effect

A particle-hole symmetric Anderson impurity model with a metallic host of narrow bandwidth is studied within the framework of the local moment approach. The resultant single-particle spectra are compared to unrestricted Hartree-Fock, second order perturbation theory about the noninteracting limit, and Lanczos spectra by Hofstetter and Kehrein. Rather accurate analytical results explain the spectral evolution over almost the entire range of interactions. These encompass, in particular, a rationale for the four-peak structure observed in the low-energy sector of the Lanczos spectra in the moderate-coupling regime. In weak coupling, the spectral evolution is governed by orbital effects, while in the strong coupling Kondo limit, the model is shown to connect smoothly to the generic Anderson impurity with a flat and infinitely wide hybridization band.Comment: 17 pages, 7 figure

Quantum Antiferromagnetism of Fermions in Optical Lattices with Half-filled p-band

We study Fermi gases in a three-dimensional optical lattice with five fermions per site, i.e. the s-band is completely filled and the p-band with three-fold degeneracy is half filled. We show that, for repulsive interaction between fermions, the system will exhibit spin-3/2 antiferromagnetic order at low temperature. This conclusion is obtained in strong interaction regime by strong coupling expansion which yields an isotropic spin-3/2 Heisenberg model, and also in weak interaction regime by Hatree-Fock mean-field theory and analysis of Fermi surface nesting. We show that the critical temperature for this antiferromagnetism of a p-band Mott insulator is about two orders of magnitudes higher than that of an $s$-band Mott insulator, which is close to the lowest temperature attainable nowadays