Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

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.

extended version with additional technical details; 5 RevTex pages, 2 figures; to appear in Phys. Rev. B

References in corpus (17)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Weak Coupling Phase Diagram of the Two Chain Hubbard Model
• The N-chain Hubbard Model in Weak Coupling
• Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model
• Self-energy and critical temperature of weakly interacting bosons
• Phases of the two-band model of spinless fermions in one dimension
• Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface
• Field-theoretical renormalization group for a flat two-dimensional Fermi surface
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Crossover to Fermi-liquid behavior for weakly-coupled Luttinger liquids in the anisotropic large-dimension limit
• Fermi surface renormalization in Hubbard ladders
• Interchain coherence of coupled Luttinger liquids at all orders in perturbation theory
• Interaction induced collapse of a section of the Fermi sea in in the zig-zag Hubbard ladder
• Dynamic scaling in the vicinity of the Luttinger liquid fixed point
• Interaction-induced Fermi surface deformations in quasi one-dimensional electronic systems
• Fermi Surface Renormalization in Two Spatial Dimensions

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• Possible phases of two coupled n-component fermionic chains
• Confined coherence in quasi-one-dimensional metals
• Conductivity between Luttinger liquids: coupled chains and bilayer graphene
• Ward Identities and chiral anomalies for coupled fermionic chains
• Ferromagnetism in one-dimensional metals: breakdown of the Hartree-Fock approximation and possible first order phase transition
• Confinement and quantum anomaly in quasi-1D spinless fermion chains
• Fermi surface renormalization and quantum confinement in the two-coupled chains model
• Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase