Fermions without Fermion Fields
- Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
It is shown that an arbitrary fermion hopping Hamiltonian can be mapped into a system with no fermion fields, generalizing an earlier model of Levin and Wen. All operators in the Hamiltonian of the resulting description commute (rather than anticommute) when acting at different sites, despite the system having excitations obeying Fermi statistics. While extra conserved degrees of freedom are introduced, they are all locally identified in the representation obtained. The same methods apply to Majorana (half) fermions, which for Cartesian lattices mitigate the fermion doubling problem. The generality of these results suggests that the observation of Fermion excitations in nature does not demand that anticommuting Fermion fields be fundamental.
- OSTI ID:
- 20699479
- Journal Information:
- Physical Review Letters, Vol. 95, Issue 17; Other Information: DOI: 10.1103/PhysRevLett.95.176407; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0031-9007
- Country of Publication:
- United States
- Language:
- English
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