6 research outputs found
Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
The exact large time and distance behavior of the field-field correlators has
been computed for one-dimensional impenetrable anyons at finite temperatures.
The result reproduces known asymptotics for impenetrable bosons and free
fermions in the appropriate limits of the statistics parameter. The obtained
asymptotic behavior of the correlators is dominated by the singularity in the
spectral density of the quasiparticle states at the bottom of the band, and
differs from the predictions of the conformal field theory. One can argue,
however, that the anyonic response to the low-energy probes is still determined
by the conformal terms in the asymptotic expansion.Comment: 5 pages, RevTeX
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
This work presents the derivation of the large time and distance asymptotic
behavior of the field-field correlation functions of impenetrable
one-dimensional anyons at finite temperature. In the appropriate limits of the
statistics parameter, we recover the well-known results for impenetrable bosons
and free fermions. In the low-temperature (usually expected to be the
"conformal") limit, and for all values of the statistics parameter away from
the bosonic point, the leading term in the correlator does not agree with the
prediction of the conformal field theory, and is determined by the singularity
of the density of the single-particle states at the bottom of the
single-particle energy spectrum.Comment: 26 pages, RevTeX
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
We have obtained a determinant representation for the time- and
temperature-dependent field-field correlation function of the impenetrable
Lieb-Liniger gas of anyons through direct summation of the form factors. In the
static case, the obtained results are shown to be equivalent to those that
follow from the anyonic generalization of Lenard's formula.Comment: 16 pages, RevTeX
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
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 , the anyonic reduced density matrices in the grand canonical
ensemble is expressed as Fredholm minors of the integral operator () with complex statistics-dependent coefficient . For we recover the bosonic case of Lenard
. Due to nonconservation of parity, the anyonic field correlators
\la \fad(x')\fa(x)\ra are different depending on the sign of .Comment: 13 pages, RevTeX
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
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, and , of the
statistics parameter , and coincide with the predictions of the
conformal field theory at low temperatures.Comment: 25 pages, RevTeX