Anomalous Hydrodynamics of Fractional Quantum Hall States

TL;DR

This paper develops a quantum hydrodynamics framework for fractional quantum Hall states, modeling the electronic fluid as vortex dynamics in an incompressible rotating liquid, capturing key FQH features including Lorentz shear stress.

Contribution

It introduces a quantized hydrodynamics approach for FQH states based on vortex dynamics, providing a new theoretical framework for understanding these quantum fluids.

Findings

Captures major features of FQH states including Lorentz shear stress

Provides a consistent quantization of vortex hydrodynamics

Offers a framework applicable to FQHE and superfluid studies

Abstract

In this paper we propose a comprehensive framework for the quantum hydrodynamics of the Fractional Quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime could be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states including the subtle effect of Lorentz shear stress. We present a consistent quantization of hydrodynamics of an incompressible fluid providing a powerful framework to study FQHE and superfluid. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.