2016/12/22 by Dung Xuan Nguyen, Tankut Can, Andrey Gromov · 1 citation
Mathematics · Physics and Astronomy · #Berry connection and curvature #Complex conjugate #Condensed matter physics #Conjugate #Duality (order theory) #Generalization #Holomorphic function #Landau quantization #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevlett.118.206602
published as Phys. Rev. Lett. 118, 206602 (2017) · 10 pages
arxiv created 2016/12/22 · openalex publication_date 2017/05/19 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 nontrivial checks of the relations, including for the Jain states and their PH conjugates.