Dynamical probes for topological and non-Hermitian systems

We present several new ways of probing topological and non-Hermitian systems with dynamical tools.

The first probe is a real-space Chern marker equivalent to the lattice charge polarization susceptibility to a circularly polarized electric field. This quantity, and other similar ones obtained from it, can be rigorously derived from a linear response theory. Furthermore, they can be defined even at nonzero temperature and realized in circular dichroism experiments.

The second probe relies on quench dynamics and can be used to determine the universality classes and critical exponents of topological phase transitions, e.g. with Dirac or nodal-loop gap closures, and compare them with the ones predicted by Kibble-Zurek scaling. Bloch state tomography reveals additional differences in the defect trajectories for sudden quenches.

The third probe is a quantum metric which gives a consistent description of non-Hermitian system dynamics through a nonstationary representation of the Hilbert space. This approach generalizes biorthogonal quantum mechanics to PT-broken cases, and enables the correct calculation of observables, as opposed to other methods in which the time evolution is obtained simply by dividing by the norm of the state. By employing the metric formalism, we further reveal unprecedented behaviors of non-Hermitian systems subjected to linear quenches, in which the defect production is frozen to a finite value even in the adiabatic limit, and the Kibble-Zurek scaling breaks down.