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Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

Sascha Ledowski·Peter Kopietz·Alvaro Ferraz
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Abstract

Using functional renormalization group methods, we present a self-consistent calculation of the true Fermi momenta k_F^a (antibonding band) and k_F^b (bonding band) of two spinless interacting metallic chains coupled by small interchain hopping. In the regime where the system is a Luttinger liquid, we find that Delta = k_F^b - k_F^a is self-consistently determined by Delta = Delta_{1} [ 1 + {g}_0^2 ln (Lambda_0 / Delta)^2]^{-1} where g_0 is the dimensionless interchain backscattering interaction, Delta_{1} is the Hartree-Fock result for k_F^{b}-k_F^a, and Lambda_0 is an ultraviolet cutoff. If {g}_0^2 ln (Lambda_0 / Delta_{1})^2 is much larger than unity than even weak interachain backscattering leads to a strong reduction of the distance between the Fermi momenta.

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Sascha Ledowski, Peter Kopietz, Alvaro Ferraz. 2005-04-12. Self-consistent Fermi surface renormalization of two coupled Luttinger liquids. https://doi.org/10.1103/physrevb.71.235106

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