The main areas of research conducted in our group are concentrated around two distinct topics: effective field theories of quantum phases of matter and universality in few-body quantum physics.
Although microscopically condensed matter physics is about interaction between electrons, protons, neutrons and light, often the many-body nature of the problem gives rise to emergence of new degrees of freedom with intriguing collective behavior at low energies. These degrees of freedom constitute the building blocks of effective field theories that in addition are constrained by symmetries of the problem. This set-up provides a reliable micro-independent framework for non-perturbative understanding of strongly interacting quantum systems. In our group we are especially interested in the interplay of topology and geometry in quantum phases of matter. We apply effective theories to various low-dimensional many-body topological quantum fluids such as chiral superfluids, superconductors and quantum Hall states.
In quantum mechanics three identical bosons in three dimensions interacting resonantly via a short-range two-body potential form an infinite tower of bound states, whose energy spectrum organizes itself into a geometric series accumulating at zero energy. This was discovered theoretically by Vitaly Efimov in 1970 and is known today as the Efimov effect. This effect is a beautiful example of few-body universality since it is independent of the detailed form of the interaction potential provided it is tuned to the resonance.
Last decade saw a wave of interest in few-body Efimov physics which was fueled by its experimental verification in cold atom experiments. Although originally predicted to occur only in three dimensional systems with short-range resonant interactions, the Efimov physics is more general.
In our group we are pushing forward the theoretical frontier of the Efimov physics focusing mainly to lower-dimensional systems.