Online Seminar: Prof Walter Hofstetter, Goethe U. Frankfurt

Correlated topological quantum states in ultracold atoms 
 

SPEAKER: Prof Walter Hofstetter

AFFILIATION: Institute for Theoretical Physics, Goethe University Frankfurt, Germany

HOSTED BY: Dr Clara Javaherian, UTS Centre for Quantum Software and Information

ABSTRACT: 
Recent years have witnessed dramatic progress in experimental control and theoretical modeling of quantum simulations with ultracold atoms. Novel developments include synthetic gauge fields for neutral atoms, induced by time-periodic driving, which allow the simulation of topologically nontrivial phases of matter with strong interactions. I will discuss recent theoretical results:

Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. We investigate the edge state emergent at a smooth topological phase boundary of interacting fermions within the time-reversal invariant Hofstadter-Hubbard model. We characterize the localization of the edge state and the topological phase boundary by means of the local compressibility, the spectral density, a generalized local spin Chern marker as well as the Hall response and find good agreement between all these quantities. We observe robustness of the edge state against fermionic two-body interactions. Hence the bulk-boundary correspondence for the interacting system is confirmed. We propose the detection of the local compressibility by using a quantum gas microscope.

We furthermore study transport properties and the topological phase transition in two-dimensional interacting, disordered systems. Within real-space dynamical mean-field theory we derive the Hall conductance, which is quantized and serves as a topological invariant for insulators, even when the energy gap is closed by localized states. In the spinful Harper-Hofstadter-Hatsugai model we find that the repulsive on-site interaction can assist weak disorder to induce the integer quantum Hall effect, and generally widens the regime of the topological phase in the disordered system.

Measuring topological invariants of interacting systems is challenging. We establish a relation of the effective topological Hamiltonian to the single-particle density matrix (SPDM) for interacting two-band systems, and design a tomography scheme for the SPDM in cold atom experiments. Thus the Chern number and the topological phase transition can be reconstructed from experimental data.