One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula

Abstract

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 A. Lenard for bosons. In the case of impenetrable but otherwise free anyons with statistical parameter $\kappa$, the anyonic reduced density matrices in the grand canonical ensemble is expressed as Fredholm minors of the integral operator ($1-\gamma {\hat{\theta }}_T$) with complex statistics-dependent coefficient $\gamma =(1+e^{\pm i\pi \kappa })/\pi$. For $\kappa =0$ we recover the bosonic case of Lenard $\gamma =2/\pi$. Due to nonconservation of parity, the anyonic field correlators $\la \fad(x')\fa(x)\ra$ are different depending on the sign of $x^{\prime }-x$.

13 pages, RevTeX 4

References in corpus (4)

• Correlation functions of one-dimensional anyonic fluids
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Bethe Ansatz for 1D interacting anyons
• Coulomb blockade of anyons

Cited by in corpus (7)

• Fermionization and bosonization of expanding 1D anyonic fluids
• Ground-state properties of one-dimensional anyon gases
• Junctions of anyonic Luttinger wires
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Quantum Inverse Scattering Method with anyonic grading