Ball, Robin. (2005) Fermions without fermion fields. Physical Review Letters, Vol.95 (No.17). ISSN 0031-9007

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Abstract

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.

Item Type:	Journal Article
Alternative Title:	Fermions without fermi fields
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Fermions, Hamiltonian systems
Journal or Publication Title:	Physical Review Letters
Publisher:	American Physical Society
ISSN:	0031-9007
Official Date:	21 October 2005
Dates:	Date Event 21 October 2005 Published
Volume:	Vol.95
Number:	No.17
Number of Pages:	4
Identification Number:	10.1103/PhysRevLett.95.176407
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
URI:	http://wrap.warwick.ac.uk/id/eprint/34431

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