Research
Overview
The main focus of my research is understanding the properties of systems with strong electron-electron interactions and correlations between the constituent particles. Strongly correlated electron systems represent an important class of quantum materials and are at the far-front of the condensed matter physics research. There have been over 40 classes of strongly-correlated electron systems (SCES) discovered already, including the high-temperature superconductors (cuprate and Fe-based superconductors), organic superconductors, heavy fermions, transition-metal dichalcogenides, and general quantum critical materials. Despite pure fundamental interest, such correlated materials are among the most technologically promising systems, with the potential to revolutionize modern industrial applications ranging from energy transmission to cooling technology, energy storage, energy generation and computer technology.
The understanding of the origin of these emergent collective behaviors represents perhaps the greatest unsolved problem in physics today and is essential for the predictive design of functional SCES and further technological progress.
The exotic properties of SCES stem from the complex interplay between charge, spin, orbital and lattice degrees of freedom and are very sensitive to changes in external parameters (e.g. temperature, pressure or doping).
Theoretical Challenges
The strong electron interactions responsible for the rich properties of SCES also make them difficult to study. In these systems, the Coulomb interaction between electrons is often of the same order of magnitude or much larger than the kinetic energy. This causes standard perturbative approaches and mean-field-like approximations to break down. On the other hand, due to the vast improvement of computational methods over the past decades, numerical analysis has now become a powerful and often the only tool for their analysis. For this reason, ongoing development and application of non-perturbative numerical many-body techniques is absolutely crucial for further progress.
Numerical approaches
The field of strongly correlated systems is very diverse. I am primarily interested in the development and application of numerical many-body algorithms for model systems. This includes the use such techniques as:
Dynamical Mean Field Theory
Dynamical Cluster Approximation
Continuous Time Quantum Monte Carlo
Typical Medium Theory for disordered systems
Lattice Models
Currently, most numerical studies of correlated systems are done on simple toy models (Hubbard model, Anderson tight-binding model). However, there is a growing recognition that theoretical analysis of many newly developed materials requires construction and study of more realistic models. Examples of the extensions are: a) long-range Coulomb and exchange interactions; b) several orbitals at each lattice site; c) crystal-field and spin-orbit splitting of the orbitals and d) disorder effects.
Driven by the need of going beyond simple model descriptions and based on my experience with both interaction and disordered systems, my current research focuses on the following three research topics:
