Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to implement a topological interface within the experimentally realizable time-reversal invariant Hofstadter model which gives rise to a topological phase boundary at the center of the system, and investigate the influence of two-body interactions on the interface in a fermionic system. The interface can in principle be probed via the spatially resolved compressibility of the system by using a quantum gas microscope. Furthermore, we distinguish the phases through their Hall response and compute a local spin Chern marker which proves the phase separation of two distinct topological many-body phases. The bulk-boundary correspondence for the interacting system is confirmed by computing the edge state spectra at the interface.

We investigate the dimensionally induced phase transition from the normal to the Bose-Einsteincondensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding is in agreement with the dominant role of quantum fluctuations in lower dimensions, as they are explicitly included in our theory. Furthermore, we determine for the 1D-3D-transition the power-law exponent of the critical temperature for two different non-interacting Bose gas models yielding the same value of 1/2, which indicates that they belong to the same universality class. For the weakly interacting Bose gas we find for both models that this exponent is robust with respect to finite interaction strengths.

The concept of the local Chern marker has gained a lot of attention especially in the field of ultracold quantum gases in optical lattices and artificial gauge fields. We investigate in further detail the microscopic real-space characteristics of the local Chern marker for the two-band Harper-Hofstadter-Hatsugai model and propose a tomographic scheme for the experimental detection of an approximate local Chern marker neglecting higher orders.

No abstract