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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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Using a non-perturbative functional renormalization group approach involving both fermionic and bosonic fields we calculate the interaction-induced change of the Fermi surface of spinless fermions moving on two chains connected by weak interchain hopping t_{bot}. We show that interchain backscattering can strongly reduce the distance Delta between the Fermi momenta associated with the bonding and the antibonding band, corresponding to a large reduction of the effective interchain hopping t_{bot}^{*} A self-consistent one-loop approximation neglecting marginal vertex corrections and wave-function renormalizations predicts a confinement transition for sufficiently large interchain backscattering, where the renormalized t_{bot}^{*} vanishes. However, a more accurate calculation taking vertex corrections and wave-function renormalizations into account predicts only weak confinement in the sense that 0< | t_{bot}^{*} | << | t_{bot} |. Our method can be applied to other strong-coupling problems where the dominant scattering channel is known.
We use Wilsons weak coupling ``momentum shell renormalization group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.
We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the t-J model in two dimensions. We use typical sets of band parameters relevant to the cuprate superconductors. The second order theory in the parameter lambda is argued to be quantitatively valid in the overdoped regime for 0 < n < 0.75 (n is the particle density). The calculation involves the self consistent solution of equations for an auxiliary Fermi liquid type Greens function and an adaptive spectral weight, or caparison factor, described in recent papers by Shastry (Refs. (1) and (5)). We present the numerical results at low as well as high T at various low to intermediate densities in the normal phase with emphasis placed on features that are experimentally accessible. We display the momentum space occupation function m(k), various energy dispersions locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions along various directions in the Brillouin zone, and with typical additional elastic scattering. The line-shapes have an asymmetric shape and a broad background that is seen in experiments near and beyond optimal hole doping, and validate approximate recent rece
We compare two fermionic renormalization group methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor mans method setup to resum ``leading-log divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional renormalization group method and leads to a set of differential equations which can only for certain setups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor mans approach seems to describe the crossover from the ``perfect to the ``open chain fixed point we collect evidence that difficulties may arise close to the ``perfect chain fixed point. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the functional renormalization group method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics.
We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub Bose-Luttinger liquids, which in some respects can be regarded as boson
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