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

Antiferromagnetic order in multi-band Hubbard models for iron-pnictides

We investigate multi-band Hubbard models for the three iron 3$d$-$t_{2g}$ bands and the two iron 3$d$-$e_g$ bands in ${\rm La O Fe As}$ by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Hartree--Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree--Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hund's-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron $e_g$ electrons polarize the $t_{2g}$ electrons and they substantially contribute to the ordered moment.Comment: 4 pages, 4 figure

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

Cluster dynamical mean field theory of quantum phases on a honeycomb lattice

We have studied the ground state of the half-filled Hubbard model on a honeycomb lattice by performing the cluster dynamical mean field theory calculations with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a `spin liquid' from the on-site interaction U=0 to $U_c$ (between $4.6t$ and $4.85t$) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semi-metallic state exits only at U=0. We further find that the magnetic phase transition at $U_c$ from the `spin liquid' to the N\'{e}el antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the `spin liquid' phase against the emergence of a magnetic order.Comment: 5 pages and 8 figure

Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions

We use Brueckner-Goldstone perturbation theory to calculate the ground-state energy of the half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbard interaction. We obtain the momentum distribution as a functional derivative of the ground-state energy with respect to the bare dispersion relation. The resulting expressions agree with those from Rayleigh-Schroedinger perturbation theory. Our results for the momentum distribution and the quasi-particle weight agree very well with those obtained earlier from Feynman-Dyson perturbation theory for the single-particle self-energy. We give the correct fourth-order coefficient in the ground-state energy which was not calculated accurately enough from Feynman-Dyson theory due to the insufficient accuracy of the data for the self-energy, and find a good agreement with recent estimates from Quantum Monte-Carlo calculations.Comment: 15 pages, 8 fugures, submitted to JSTA

Fermi-Hubbard physics with atoms in an optical lattice

The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answer important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid and Mott-insulating regimes.Comment: Posted with permission from the Annual Review of of Condensed Matter Physics Volume 1 \c{opyright} 2010 by Annual Reviews, http://www.annualreviews.or

Exact diagonalization study of optical conductivity in two-dimensional Hubbard model

The optical conductivity \sigma(\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} X \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} X \sqrt{18} cluster, but different from 4 X 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.Comment: 5 pages, 5 figure

Role of Diffusion in Two-dimensional Bimolecular Recombination

Experiments on carrier recombination in two-dimensional organic structures are often interpreted in the frame of the Langevin model with taking into account only the drift of the charge carriers in their mutual electric field. While this approach is well justified for three-dimensional systems, it is in general not valid for two-dimensional structures, where the contribution of diffusion can play a dominant role. We study the two-dimensional Langevin recombination theoretically and find the critical concentration below which diffusion cannot be neglected. For typical experimental conditions, neglecting the diffusion leads to an underestimation of the recombination rate by several times.Comment: 3 pages, 1 figur