Spin Hamiltonian for which quantum hall wavefunction is exact
A Hamiltonian is introduced for which the spin-1/2 quantum liquid wavefunction proposed by Kalmeyer and Laughlin is the exact ground state. An explicit proof is given that this state is a doubly degenerate spin singlet. The excitation spectrum of the Hamiltonian is calculated variationally and a case is made for the presence of an energy gap. The spin-1 collective mode, calculated in the single-mode approximation, is shown to have a large energy that is minimized at the Brillouin zone corner. The spin-0 collective mode behaves similarly but has lower overall energy. Wavefunctions for the neutral spin-1/2 excitations are shown to form an exact spin doublet. The energy of a pair of such excitations increases or decreases logarithmically with separation depending on the total spin. When widely separated, the excitations possess an internal 2-fold degree of freedom, a Brillouin zone that is half the linear dimension of the full zone, and a mass comparable to that of the collective modes. /copyright/ Academic Press, Inc. 1989
- Research Organization:
- Department of Physics, Stanford University, Stanford, California 94305, and Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (US)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5873253
- Journal Information:
- Ann. Phys. (N.Y.); (United States), Vol. 191:1
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
SOLIDS
COLLECTIVE EXCITATIONS
ANNIHILATION OPERATORS
BRILLOUIN ZONES
CORRELATION FUNCTIONS
DEGREES OF FREEDOM
GROUND STATES
HALL EFFECT
HAMILTONIANS
MAGNETIC MATERIALS
MONTE CARLO METHOD
SUM RULES
WAVE FUNCTIONS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EXCITATION
FUNCTIONS
MATERIALS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
ZONES
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)