One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations

Abstract

Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely characterizing the correlators. The system is the same as the one for impenetrable bosons but with different initial conditions. The large-distance asymptotic behavior of the correlation functions is obtained from the analysis of the Riemann-Hilbert problem associated with the system of differential equations. We calculate both the exponential and pre-exponential factors in the asymptotics of the field-field correlators. The asymptotics derived in this way agree with those of the free fermions and impenetrable bosons in the appropriate limits, $\kappa \to 1$ and $\kappa \to 0$, of the statistics parameter $\kappa$, and coincide with the predictions of the conformal field theory at low temperatures.

25 pages, RevTeX 4

References in corpus (14)

• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Fermionization and bosonization of expanding 1D anyonic fluids
• Correlation functions of one-dimensional anyonic fluids
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Ground-state properties of one-dimensional anyon gases
• Bethe Ansatz for 1D interacting anyons
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Coulomb blockade of anyons
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Quantum Inverse Scattering Method with anyonic grading
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures

Cited by in corpus (18)

• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Strongly interacting mesoscopic systems of anyons in one dimension
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• 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
• Correlation functions of one-dimensional strongly interacting two-component gases
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Effective free-fermionic form factors and the XY spin chain
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Anyon Quantum Transport and Noise away from Equilibrium
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Dualities for anyons