Numerical approach to strongly interacting spins and fermions. Working with postdocs and students, I have been building and testing novel numerical algorithms to describe interacting quantum systems. For interacting Fermi gases and quantum spin models, we pursue massive parallelization of functional renormalization group (FRG). FRG treats all competing orders in interacting quantum systems on equal footing, making it possible to reliably predict the phase diagram. For quantum spin models, we use two complementary ansatz where the many-body wavefunction is represented by tensor networks or neural networks. The main goal is to find the ground state and extract the order (or the lack thereof) from an unbiased variational approach.

Entanglement and dynamics of open quantum systems.  I am also interested in the topological properties of quantum dynamics, for example the time evolution following a quantum quench (a sudden change in the Hamiltonian) and periodically driven quantum systems (known as Floquet systems). A closely related subject is open quantum systems described by non-Hermitian Hamiltonians. For example, we were able to establish some rigorous relations for links, knots, and various incarnations of monopoles hidden in quantum dynamics.