2008/01/31 by Ovidiu I. Patu, Ovidiu I Pâţu, Vladimir E. Korepin +3 · 4 citations
Mathematics · Physics and Astronomy · #Anyon #Fermion #Fredholm determinant #Generalization #Operator (biology) #Quantum and electron transport phenomena #Quantum many-body systems #Sign (mathematics) #Spectral Theory in Mathematical Physics #Topological quantum computer #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/14/145006
published as J. Phys. A: Math. Theor. 41 (2008) 145006 · 13 pages, RevTeX 4
openalex publication_date 2008/03/26 · arxiv created 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have obtained an expansion of the reduced density matrices (or, equivalently, correlation functions of the fields) of impenetrable one-dimensional anyons in terms of the reduced density matrices of fermions using the mapping between anyon and fermion wavefunctions. This is the generalization to anyonic statistics of the result obtained by Lenard (1966 J. Math. Phys. 7 1268) for bosons. In the case of impenetrable but otherwise free anyons with statistics parameter κ, the anyonic reduced density matrices in the grand canonical ensemble are expressed as Fredholm minors of the integral operator with the complex statistics-dependent coefficient γ = (1 + e ±iπκ )/π. For κ = 0 we recover the bosonic case of Lenard γ = 2/π. Due to nonconservation of parity, the anyonic field correlators ⟨Ψ† A ( x ')Ψ A ( x )⟩ are different depending on the sign of x ' − x .