Dynamic scaling in the vicinity of the Luttinger liquid fixed point

We calculate the single-particle spectral function A (k, omega) of a one-dimensional Luttinger liquid by means of a functional renormalization group (RG) approach. Given an infrared energy cut-off Lambda = Lambda(0)e(-1), our approach yields the spectral function in the scaling form, A(Lambda) (k(F) + p, omega) = tau Z(1)A(1) (pxi, omegatau), where k(F) is the Fermi momentum, Z(1) is the wavefunction renormalization factor, tau = 1/Lambda is the timescale and xi = nu(F)/Lambda is the length scale associated with Lambda. At the Luttinger liquid fixed point (l --> infinity) our RG result for A(k, omega) exhibits the correct anomalous scaling properties, and for k = +/- k(F) agrees exactly with the well known bosonization result at weak coupling. Our calculation demonstrates that the field rescaling is essential for obtaining the crossover from Fermi liquid behaviour to Luttinger liquid behaviour from a truncation of the hierarchy of exact RG flow equations as the infrared cut-off Lambda is reduced.