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

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