TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.4.159
TI  - Adiabatic deformations of quantum Hall droplets
PY  - 2023/10/13
UR  - https://www.scipost.org/SciPostPhys.15.4.159
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 4
SP  - 159
A1  - Oblak, Blagoje
AU  - Estienne, Benoit
AB  - We consider area-preserving deformations of the plane, acting on electronic wave functions 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 ($\propto N^2$ 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.
ER  -

@Article{10.21468/SciPostPhys.15.4.159,
	title={{Adiabatic deformations of quantum Hall droplets}},
	author={Blagoje Oblak and Benoit Estienne},
	journal={SciPost Phys.},
	volume={15},
	pages={159},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.4.159},
	url={https://scipost.org/10.21468/SciPostPhys.15.4.159},
}