Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

TL;DR

This paper uses functional renormalization group methods to self-consistently calculate the true Fermi momenta in two coupled Luttinger liquids, revealing how weak interchain interactions can significantly reduce Fermi surface splitting.

Contribution

It introduces a self-consistent approach to determine Fermi momenta in coupled Luttinger liquids, accounting for interaction effects beyond Hartree-Fock approximation.

Findings

Weak interchain backscattering can strongly reduce Fermi momentum difference.

The self-consistent formula relates Fermi momenta difference to interaction strength.

Interaction effects can dominate even when coupling is weak.

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.