Numerical Approaches to Strongly Correlated Materials

Strongly correlated many-body systems are at the forefront of theoretical and experimental research in condensed matter physics. They have become increasingly important since refined experimental techniques allow to study and exploit subtle physical effects, which sometimes enable big technological applications. Particularly fascinating novel materials, whose physical properties are governed by many-body effects are the cuprates, manganites and vanadates. The most renowned effects are superconductivity and the so-called colossal magnetoresistance, of great interest for magnetic storage devices (hard disks). These systems are highly complex and possess a rich phase diagram originating from the interplay of several quantum degrees of freedom: correlated electrons, local spins, orbitals and phonons. The theoretical description of these complex materials poses many challenging problems. Some of their physical properties are by now understood theoretically, at least qualitatively; many effects, however, are still an open issue. The purpose of the present project is to address such open questions by state-of-the-art numerical techniques. Numerical simulations have proven extremely useful during the last two decades in the study of isolated features of novel materials. Despite the success of these techniques, they still suffer from various shortcomings. Part of our project is the development and improvement of such techniques in order to extend their applicability within the aforementioned novel materials. Our numerical simulations will be based on Finite Temperature Exact Diagonalization, Quantum Monte Carlo, and Cluster Perturbation Theory, chosen according to their suitability for a particular model, its parameters, and the system size. We will also aim at developing an effective model to enable the simultaneous simulation of all relevant degrees of freedom for a unified description of the complex physical phenomena in these materials.

The focus of the present research project was the theoretical investigation of novel strongly correlated materials, such as manganites, vanadates and cuprates. The properties of these materials are caused by mobile charge carriers, localized magnetic moments, lattice vibrations and orbital fluctuations. The interplay of these degrees of freedom results in a rich phase diagram which shows different types of magnetic order, like paramagnetism, ferromagnetism and antiferromagnetism. The magnetic phases are accompanied by isolating and metallic behavior, respectively. The notion `strong correlations` is used if the physical effects originate from the interaction of the various constituents and cannot be described by isolated components of the system. The most prominent effect of the manganites is the so-called `colossal magneto resistance`, i.e. a very pronounced dependence of the resistivity on the external magnetic field. For the computer simulation of such a great number of different degrees of freedom it was necessary to construct effective simplified physical models, as well as to extend and improve existing numerical procedures. Within the scope of the project we succeeded in developing algorithms which allow the exact computation of physical properties of small systems of strongly correlated particles for arbitrary temperature. In addition, it was possible to study infinite systems by combining such exact diagonalization results for finite systems via cluster perturbation theory. As far as (Quantum-) Monte Carlo simulations are concerned, we developed a novel exact procedure in order to treat multimodal potentials, which cannot be addressed reliably by standard approaches. Another important breakthrough could be achieved for the simultaneous quantum mechanical simulation of electrons and phonons. We succeeded in reducing the notoriously huge simulation times for phonons by several orders of magnitude. An important by-product of the project was the numerical improvement of the maximum entropy method, which provides the only consistent approach to ill-posed inversion problems. Such problems occur, among others, in the data analysis of Quantum-Monte Carlo simulations. During the project a wide variety of physical properties of manganites and vanadates has been studied and interesting - and partially unexpected - results could be achieved, such as the existence of ferromagnetic polarons as opposed to of phase separation. In the frame of this project significant contributions could be achieved allowing a deeper understanding of strongly correlated many-body systems.