Nonperturbative methods for studying dressed quasiparticles and their effective interactions in strongly-coupled systems

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An electron moving through a solid is intimately connected with all of its elementary excitations, such as lattice vibrations, and it drags along, as it moves, a cloud of such possible excitations. This complex entity is called a "dressed quasiparticle". Compared to the original electron, it has a different effective mass and dynamical properties. The interactions between dressed quasiparticles are also very different from those between the original electrons: exchange of excitations between their clouds mediates an effective attraction that may result in superconductivity or other interesting behavior. Understanding the nature of these dressed quasiparticles and their effective interactions, and their combined effect on the physical properties of the solid, are fundamental questions that drive a lot of the modern research in theoretical condensed matter and materials physics.***Over the past decade, my research program has been focused on finding highly accurate yet computationally inexpensive approximations for describing such quasiparticles and their interactions in strongly coupled regimes where perturbative methods fail. My group has succeeded in developing such methods based on variational principles and proving their accuracy by comparison with highly accurate numerical results for simple models, where the latter are available. We have also used these methods to uncover very unexpected behavior in certain types of models that had not been investigated before because their complexity makes them difficult for numerical studies. ***During the next five years, my main goals are:***a) to use the methods already developed in my group to propose and study realistic effective models of various interesting materials, in particular those that fall in the so-called "strongly correlated" regime. These cannot be studied by perturbative means, and numerical studies are often restricted to rather small clusters and/or high temperatures, and may not be relevant for the physics of interest. Such materials, which include cuprates, manganites, iridates, pnictides, but also organic and even biological systems, exhibit a rich variety of properties like high-temperature superconductivity, colossal magnetoresistivity, quantum coherence at high temperatures, etc., that are still not understood. ***b) to generalize these methods to systems with a finite concentrations of particles coupled to various types of excitations. This would allow us to understand how accurate are the effective models that correctly incorporate the quasiparticles' dynamics and their effective interactions, as calculated in the few-particle regime. It would also represent a significant advancement in understanding the properties of such models, which are relevant for describing some of the most fascinating materials and yet little is known about their generic behavior away from the weakly-coupled regime. **