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Dynamical quantum Hall effect in the parameter space
1Physics Department, University of Fribourg, Chemin du Musee 3, 1700 Fribourg, Switzerland.
Summary
Researchers demonstrate observing the Berry phase in generic quantum systems beyond weakly interacting particles. This nonadiabatic response to parameter changes reveals a dynamical quantum Hall effect, observed in spin chains as a rotational quantum Hall effect.
Area of Science:
- Quantum Mechanics
- Condensed Matter Physics
- Geometric Phases
Background:
- Geometric phases, such as the Berry phase, are crucial in quantum mechanics, typically observed in adiabatic evolution of weakly interacting systems.
- Current limitations restrict Berry phase measurements to systems amenable to interference experiments.
Purpose of the Study:
- To extend the observation and measurement of Berry curvature and Berry phase to generic quantum systems.
- To establish a nonadiabatic method for detecting geometric phases.
Main Methods:
- Analyzing the nonadiabatic response of physical observables to the rate of change of external parameters.
- Investigating interacting spin chains subjected to a rotating magnetic field.
Main Results:
- Observed Berry curvature and Berry phase as a nonadiabatic response in generic systems.
- Demonstrated a quantized response analogous to the quantum Hall effect in parameter space, termed the rotational quantum Hall effect.
- Experimental verification in interacting spin chains under a rotating magnetic field.
Conclusions:
- The study overcomes limitations of traditional Berry phase measurements, enabling observations in more complex systems.
- The findings establish a connection between geometric phases and nonadiabatic dynamics, analogous to the quantum Hall effect.
- The rotational quantum Hall effect provides a new framework for understanding and measuring geometric phases in diverse quantum systems.
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