Particle-Hole Duality in the Lowest Landau Level

TL;DR

This paper establishes exact relations between response functions of fractional quantum Hall states and their particle-hole conjugates, revealing a precise duality and enabling property calculations of conjugate states.

Contribution

The authors derive a set of exact relations linking response functions of chiral quantum Hall states and their particle-hole conjugates, generalizing Girvin's construction.

Findings

Derived exact relations for Hall conductivity and viscosity

Established duality between chiral quantum Hall states and their PH-conjugates

Validated relations with Jain states and their conjugates

Abstract

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several non-trivial checks of the relations, including for the Jain states and their PH-conjugates.