Quantum mechanics of the fractional-statistics gas: Hartree-Fock approximation

• Published in: Physical review. B, Condensed matter Vol. 40; no. 13; pp. 8745 - 8758
• Main Authors: HANNA, C. B, LAUGHLIN, R. B, FETTER, A. L
• Format: Journal Article
• Language: English
• Published: Woodbury, NY American Physical Society 01-11-1989; American Institute of Physics
• Subjects: 656100 - Condensed Matter Physics- Superconductivity; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; CHARGE CARRIERS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Condensed matter: electronic structure, electrical, magnetic, and optical properties; ENERGY GAP; ENERGY LEVELS; ENERGY-LEVEL TRANSITIONS; Exact sciences and technology; EXCITATION; FERMI GAS; FERMI STATISTICS; FLUIDS; GASES; GROUND STATES; HARTREE-FOCK METHOD; MECHANICS; PHYSICAL PROPERTIES; Physics; QUANTUM MECHANICS; QUASI PARTICLES; Superconductivity; SUPERCONDUCTORS; Theory and models of superconducting state; THERMODYNAMIC PROPERTIES; TRANSITION TEMPERATURE; TWO-DIMENSIONAL CALCULATIONS; Filling coefficient; Density of states; Fermion system; Landau level; Superconductivity; Theoretical study; Ground state; Hartree Fock method; Two dimensional model; Superfluidity; Vortex; Hamiltonian
• ISSN: 0163-1829; 1095-3795
• DOI: 10.1103/PhysRevB.40.8745

The two-dimensional ideal gas of particles obeying {nu} fractional statistics is transformed to the Fermi representation and studied in the Hartree-Fock approximation. The extremal ground state is shown to be composed of Landau orbitals. When the filling factor (1{minus}{nu}){sup {minus}1} of the ground state is an integer, a logarithmically large energy gap appears in the single-particle excitation spectrum, and the particle and hole states are charged vortices with circulation {plus minus}(1{minus}{nu}){ital h}/{ital m}. The linear dependence of the total energy on the density, together with the presence of this gap, suggests that the true ground state at these fractions is a superfluid.