###### Content

# Interacting particles and flat bands: lattice models with quantum Hall analogues

### Vito Scarola, Virginia Tech, Blacksburg, USA

#### 29.11.2019 at 09:00

In certain strongly correlated quantum systems inter-particle interactions can dominate to a point where interesting many-body effects arise solely from interaction. The preeminent examples, fractional quantum Hall states, have emergent properties, including, for example, fractional charge. I will review work in our group that studies minimal lattice models hosting flat kinetic energy bands that emphasize the role of inter -particle interactions. In one study, we model spin-orbit coupled fermions in a one-dimensional flat-band optical lattice. We introduce an effective Luttinger liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge. In a separate set of studies, we use exact diagonalization and mean -field theory to examine two-dimensional lattice models with quadratic band crossing points and flat bands. Here we find that interactions open a gap and stabilize a topological Mott insulator, a state which spontaneously breaks time reversal symmetry to establ ish a quantized Hall effect in the absence of external fields. In both of these studies we explore how flat-band lattice models reveal effects analogous to those found in quantum Hall regimes.

Room 450, Theresienstr. 37