Anyon representation of the ground-state degeneracy of the quantum frustrated XY model

Journal Article · Sun Mar 01 04:00:00 EST 1992 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.45.5737· OSTI ID:7047491

Diamantini, M C; Sodano, P ^[1]

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1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We use the extension of the Jordan-Wigner transformation to planar systems to investigate the quantum frustrated {ital XY} model for spin 1/2 on a square lattice. We find that this model is mapped into the hopping Hamiltonian for a planar spinless electron in a transverse magnetic field. When we fix the frustration parameter to be a rational number such that the electron density is proportional to the total flux threading the plaquette, the model is equivalent to a {ital Z}{sub {ital N}} gauge theory of anyons. The {ital Z}{sub {ital N}} symmetry of the anyon theory implies a degeneracy 2{ital N} for the ground state of the model considered. Since we regard the frustration field as classical background, our approach has to be considered as a mean-field theory of the frustrated spin model. We briefly discuss the effect of quantum corrections to the ground-state degeneracy.

• OSTI ID: 7047491
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 45:10; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY LEVELS
GAUGE INVARIANCE
GROUND STATES
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MEAN-FIELD THEORY
PHYSICAL PROPERTIES
QUANTIZATION
QUASI PARTICLES
STATISTICAL MODELS
SUPERCONDUCTIVITY