Adiabatic Deformations of Quantum Hall Droplets

TL;DR

This paper investigates how adiabatic area-preserving deformations of quantum Hall droplets induce Berry phases, revealing a connection to Hall viscosity and proposing experimental setups for observation.

Contribution

It introduces a formalism for calculating Berry phases under quantum Hall droplet deformations, including interactions, and links these phases to Hall viscosity.

Findings

Berry phases can be expressed in terms of current and density.

Leading phase term is a super-extensive Aharonov-Bohm contribution.

Hall viscosity is incorporated into the formalism and can be observed experimentally.

Abstract

We consider area-preserving deformations of the plane, acting on electronic wavefunctions through "quantomorphisms" that change both the underlying metric and the confining potential. We show that adiabatic sequences of such transformations produce Berry phases that can be written in closed form in terms of the many-body current and density, even in the presence of interactions. For a large class of deformations that generalize squeezing and shearing, the leading piece of the phase is a super-extensive Aharonov-Bohm term (proportional to N$^2$ for N electrons) in the thermodynamic limit. Its gauge-invariant subleading partner only measures the current, whose dominant contribution to the phase stems from a jump at the edge in the limit of strong magnetic fields. This results in a finite Berry curvature per unit area, reminiscent of the Hall viscosity. We show that the latter is in fact included in our formalism, bypassing its standard derivation on a torus and suggesting realistic experimental setups for its observation in quantum simulators.