Y. Tsukamoto et al., CRITICAL-BEHAVIOR OF TOMONAGA-LUTTINGER LIQUIDS WITH A MOBILE IMPURITY, Physical review. B, Condensed matter, 58(7), 1998, pp. 3633-3640
The critical properties of Tomonaga-Luttinger liquids including a mobi
le impurity are studied by means of the Bethe ansatz method, conformal
field theory (CFT), and bosonization. We calculate conformal dimensio
ns by performing the CFT analysis of the energy spectrum for an integr
able impurity model, and show that this system is classified as c = 1
shifted Gaussian CFT. The exact critical exponents of various correlat
ion functions are obtained as functions of the impurity mass and its m
omentum. Passing to the continuum limit, we then construct an effectiv
e held theory in terms of bosonization, and directly calculate some co
rrelation functions. A possible application to the Fermi-edge singular
ity in quantum wires is also discussed.