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Dynamic scaling in the vicinity of the Luttinger liquid fixed point

Tom Busche·Lorenz Bartosch·Peter Kopietz
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Abstract

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 cutoff Lambda = Lambda_0 e^{- l}, our approach yields the spectral function in the scaling form, A_Λ (k_F + p, omega) = tau Z_l tilde{A}_l (p xi, omega tau), where k_F is the Fermi momentum, Z_l is the wave-function renormalization factor, tau = 1 / Λis the time scale and xi = v_F / Λis the length scale associated with Lambda. At the Luttinger liquid fixed point (l rightarrow infty) our RG result for A (k, omega) exhibits the correct anomalous scaling properties, and for k = \pm 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 behavior to Luttinger liquid behavior from a truncation of the hierarchy of exact RG flow equations as the infrared cutoff is reduced.

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Tom Busche, Lorenz Bartosch, Peter Kopietz. 2002-02-11. Dynamic scaling in the vicinity of the Luttinger liquid fixed point. https://doi.org/10.1088/0953-8984%2F14%2F36%2F309

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