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 (12)

• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Correlation functions of one-dimensional anyonic fluids
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Increasing of entanglement entropy from pure to random quantum critical chains
• Bethe Ansatz for 1D interacting anyons
• Bosonization at Finite Temperature and Anyon Condensation
• Coulomb blockade of anyons
• Anyons and the Bose-Fermi duality in the finite-temperature Thirring model
• Do anyons solve Heisenberg's Urgleichung in one dimension

Cited by in corpus (38)

• Fermionization and bosonization of expanding 1D anyonic fluids
• Junctions of anyonic Luttinger wires
• Ground-state properties of one-dimensional anyon gases
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Bosonic continuum theory of one-dimensional lattice anyons
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Strongly interacting mesoscopic systems of anyons in one dimension
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Quantum entanglement of particles on a ring with fractional statistics
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• Ground state properties of hard-core anyons in a harmonic potential
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
• Effective free-fermionic form factors and the XY spin chain
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Quantum Inverse Scattering Method with anyonic grading
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Dualities for anyons
• Thermodynamics of Statistical Anyons
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Two-spinon effects on the thermal Tonks-Girardeau gas