Optical data is encoded with information on the microscopic interaction between charge carriers. For an electron-phonon system, the Eliashberg equations apply and a Kubo formula can be used to get the infrared conductivity. The task of extracting the electron-phonon spectral density $\alpha^2F(\omega)$ from data is rather complicated and, thus, simplified but approximate expressions for the conductivity have often been used. We test the accuracy of such simplifications and also discuss the advantages and disadvantages of various numerical methods needed in the inversion process. Normal and superconducting state are considered as well as boson exchange mechanisms which might be applicable to the High-$T_c$ oxides.Comment: 21 pages, 14 figures; accepted for publication by Phys. Rev.

The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the singleparticle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.

We investigate the interplay between spin and orbital correlations in monolayer and bilayer manganites using an effective spin-orbital t-J model which treats explicitly the eg orbital degrees of freedom coupled to classical t2g spins. Using finite clusters with periodic boundary conditions, the orbital many-body problem is solved by exact diagonalization, either by optimizing spin configuration at zero temperature, or by using classical Monte-Carlo for the spin subsystem at finite temperature. In undoped two-dimensional clusters, a complementary behavior of orbital and spin correlations is found -the ferromagnetic spin order coexists with alternating orbital order, while the antiferromagnetic spin order, triggered by t2g spin superexchange, coexists with ferro-orbital order. With finite crystal field term, we introduce a realistic model for La1−xSr1+xMnO4, describing a gradual change from predominantly out-of-plane 3z 2 − r 2 to in-plane x 2 − y 2 orbital occupation under increasing doping. The present electronic model is sufficient to explain the stability of the CE phase in monolayer manganites at doping x = 0.5, and also yields the C-type antiferromagnetic phase found in Nd1−xSr1+xMnO4 at high doping. Also in bilayer manganites magnetic phases and the accompanying orbital order change with increasing doping. Here the model predicts C-AF and G-AF phases at high doping x > 0.75, as found experimentally in La2−2xSr1+2xMn2O7.

We present an extensive numerical study of the ferromagnetic Kondo lattice model with quantum mechanical S = 3/2 core spins. We treat one orbital per site in one dimension using the density matrix renormalization group and include on-site Coulomb repulsion between the electrons. We examine parameters relevant to manganites, treating the range of low to intermediate doping, 0 x < 0.5. In particular, we investigate whether quantum fluctuations favor phase separation over the ferromagnetic polarons observed in a model with classical core spins. We obtain very good agreement of the quantum model with previous results for the classical model, finding separated polarons which are repulsive at short distance for finite t2g superexchange J ′ . Taking on-site Coulomb repulsion into account, we observe phase separation for small but finite superexchange J ′ , while for larger J ′ polarons are favored in accordance with simple energy considerations previously applied to classical spins. We discuss the interpretation of compressibilities and present a phase diagram with respect to doping and the t2g superexchange parameter J ′ with and without Coulomb repulsion.

We study a two-dimensional effective orbital superexchange model derived for strongly correlated eg electrons coupled to t2g core spins in layered manganites. One finds that the ferromagnetic (FM) and antiferromagnetic (AF) correlations closely compete, and small changes of parameters can switch the type of magnetic order. For the same reason, spin order is easily destroyed with rising temperature, while alternating orbital correlations can persist to temperatures where FM order has already melted. A scenario for the AF phase observed in LaSrMnO4 is presented. , where ferromagnetic (FM) ab planes are stacked antiferromagnetically in the undoped case (one electron per site, x = 0). As for their 3D counterparts, the properties of the layered systems are strongly influenced by the orbital degrees of freedom of e g electrons which couple to the spins and thus influence the magnetic order. For x = 0, the hopping of e g electrons is blocked by large Coulomb interaction U , and charge fluctuations are quenched. They may be treated by second order perturbation theory which leads to virtual d