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Dynamical quantum Hall effect in the parameter space

Gritsev , V. ; Polkovnikov , A.

Proceedings of the National Academy of Sciences of the United States of America, 2012, Vol.109(17), pp.6457-6462 [Periódico revisado por pares]

National Academy of Sciences 2012

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  • Título:
    Dynamical quantum Hall effect in the parameter space
  • Autor: Gritsev , V. ; Polkovnikov , A.
  • Assuntos: Mechanics ; Magnetic Fields ; Electric Field
  • É parte de: Proceedings of the National Academy of Sciences of the United States of America, 2012, Vol.109(17), pp.6457-6462
  • Descrição: 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. ; p. 6457-6462.
  • Editor: National Academy of Sciences
  • Data de publicação: 2012
  • Idioma: Inglês

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