On the real-space detection of topology through bulk dynamics
The main subject of this talk is devoted to ongoing non-equilibrium experiments linking dynamical properties to the invariant of symmetry-protected topological phases. In our recent work https://arxiv.org/abs/2001.09074, we consider a particular protocol to read-out the winding-number of arbitrary 1D chiral models based on tracking the time-evolved density of an excitation. We show that a readily observable quantity named mean chiral displacement (MCD) gives direct access to the winding number of a non-interacting Fermi sea, and study the behavior of the MCD in interacting fermionic Su-Schrieffer-Heeger (SSH) wires by means of Matrix Product States simulations: If the wires display short-range correlations only, the MCD is shown to provide a faithful readout of the corresponding topological phase diagram. When longer-range correlations appear, the corresponding phase diagram contains trivial insulator, topological insulator, and a symmetry-breaking phase and the time-traces of the MCD are considerably different in each of the three phases thus providing a reliable tool to easily read-out the underlying phases of matter.
Then, if time permits, we may explore a general (but counterintuitive) effect found in 1D ladder setups which is presented in https://arxiv.org/abs/1911.11160: the enhancement of particle mobility through repulsive interactions.