Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas

Abstract

We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large time and long distance behavior of these objects we use effective form factor approach. The asymptotic behavior is different in the space-like and time-like regions. In particular, in the time-like region we observe the additional power factor on top of the exponential decay. We argue that this result is universal as it is related to the discontinuous behavior of the phase shift function of the effective fermions. At particular values of the anyonic parameter we recover asymptotics of spin-spin correlation functions in XXO quantum chain.

12 pages, 4 figures

References in corpus (26)

• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Universal theory of nonlinear Luttinger liquids
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Correlation functions and transport coefficients in generalised hydrodynamics
• Anyonic interferometry and protected memories in atomic spin lattices
• Form factor expansion for thermal correlators
• Green's function for magnetically incoherent interacting electrons in one dimension
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Impurity Green's function of a one-dimensional Fermi-gas
• Finite-Temperature Form Factors: a Review
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
• Density form factors of the 1D Bose gas for finite entropy states
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Correlation functions of one-dimensional bosons at low temperature
• Correlation functions of one-dimensional strongly interacting two-component gases
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Effective free-fermionic form factors and the XY spin chain
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Long time thermal asymptotics of nonlinear Luttinger liquid from inverse scattering

Cited by in corpus (12)

• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Mobile impurity in a one-dimensional gas at finite temperatures
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• On Landauer--Büttiker formalism from a quantum quench
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Dynamical correlation functions in the Ising field theory
• Triple Antidot Molecules