2004/09/30 by R. C. Ball · 9 citations
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.95.176407
published as Phys.Rev.Lett. 95 (2005) 176407 · 4 pages, submitted to PRL 18 Sept 2004; typos in equation (3) corrected 29 Sept 2004 - thanks to DR Daniels; this version as resubmitted to PRL 4 Aug 05 and accepted 6 Sept 05
arxiv created 2005/09/08 · openalex publication_date 2005/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.