Dynamical Quantum Hall Effect in the Parameter Space

TL;DR

This paper demonstrates how to observe Berry curvature and phase in generic quantum systems through non-adiabatic responses, revealing a dynamical quantum Hall effect in parameter space, extending beyond traditional weakly interacting systems.

Contribution

It introduces a method to measure Berry curvature via non-adiabatic responses, enabling observation of quantum Hall effects in complex, interacting quantum systems.

Findings

Observation of quantized response in interacting spin chains

Identification of a dynamical quantum Hall effect in parameter space

Extension of Berry phase measurement techniques to generic systems

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 non-adiabatic 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 term the rotational quantum Hall effect.