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Media type:
E-Article
Title:
Dynamical quantum Hall effect in the parameter space
Contributor:
Gritsev, V.;
Polkovnikov, A.
Published:
Proceedings of the National Academy of Sciences, 2012
Published in:
Proceedings of the National Academy of Sciences, 109 (2012) 17, Seite 6457-6462
Language:
English
DOI:
10.1073/pnas.1116693109
ISSN:
1091-6490;
0027-8424
Origination:
Footnote:
Description:
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.