The research in our group is situated at the boundary between cold gases, condensed matter and computational physics. We are interested in first principles quantitative approaches to strongly correlated many-body systems. Combining these three fields often offers a new perspective on long-standing problems.
Cold gases are systems that are ideally suited to implement prototypical strongly-correlated models in an experiment thanks to their cleanliness, tunability and the control one has over them. In other words, they can be used as quantum simulators. We are interested in a quantitative description of such systems in order to perform the necessary benchmarking steps of these analog devices. This has been successfully undertaken for a variety of systems in different contexts.
In the picture, a comparison between simulations and experiment is shown for time-of-flight images of the three-dimensional Bose-Hubbard model for 5 different temperatures. The lack of any visible difference between the two results shows the degree of control we have over these systems. See more in the original publication.
Regarding condensed matter physics we study the properties of Helium-4 and supersolids. A supersolid is an elusive phase of matter that simultaneously displays crystalline and superfluid order. According to quantum mechanics, this is perfectly allowed, but hard to find experimentally. Solid Helium-4 had been suggested as a prime candidate, but consensus is growing that it remains an insulator. However, such defects as grain boundaries and dislocations may under certain conditions support superflow. Disordered bosonic systems are also of special interest to us, featuring the Bose glass phase, which is compressible and gapless but nevertheless an insulator. We are also working on dimensional crossovers, both for bosons and fermions, which are relevant for low-dimensional (super)conductors and have recently started investigating Renyi entropies and entanglement properties.
Often algorithmic and technical advances in numerical methods are needed in order to arrive at new results. These methods include path integral Monte Carlo (PIMC) with worm-type updates, determinant Monte Carlo (detMC), diagrammatic Monte Carlo (diagMC), and dynamical mean-field theory (DMFT) and cluster extensions for bosons and fermions. PIMC works extremely well for bosonic systems, whereas detMC is well suited for fermionic systems at half filling. These methods fail for general fermionic problems because of the sign problem. In diagMC we explore the possibilities a sampling of the Feynman series (which has a sign problem that is not volume dependent) might offer for strongly correlated systems. In the DMFT approach we go in another direction: The system is solved selfconsistently for a small cluster while preserving information in Matsubara domain. If big enough clusters can be studied, the thermodynamic answer may be found after extrapolation in the cluster size.