Particle-Hole Conjugation

Hiroshi Watanabe

James S. Bell

宗武 長谷川

Dung Xuan Nguyen, Tankut Can, Andrey Gromov

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.

G E Stedman

The application of quasispin in nuclear, atomic and ligand field theory is extended here to systems of electron and hole states in a metallic systems. Conversely, results known in connection with particle-hole conjugation in metals are generalised to shell theoretic applications of quasispin. The analogy between the relationship of particle hole conjugation with quasispin and the relationship of time reversal with ordinary spin is extended to the development of selection rules parallelling those associated through Kramers with time reversal. Hamiltonians such as the BCS Hamiltonian which are composed of quasispin operators with real or imaginary coefficients have definite conjugation signature and so have a special interest. Several old and new results for matrix elements within a half-filled shell are derived from this viewpoint.