title: Dynamical quantum Hall effect in the parameter space.
abstract: Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect.
authors.affiliation: Physics Department, University of Fribourg, Chemin du Musee 3, 1700 Fribourg, Switzerland.
authors.forename: V
authors.initials: V
authors.lastname: Gritsev
authors.forename: A
authors.initials: A
authors.lastname: Polkovnikov