Anomalous scaling and spin-charge separation in coupled chains

We use a bosonization approach to show that the three dimensional Coulomb interaction in coupled metallic chains leads to a Luttinger liquid for vanishing inter-chain hopping $t_{\bot}$, and to a Fermi liquid for any finite $t_{\bot}$. However, for small $t_{\bot} \neq 0$ the Greens-function satisfies a homogeneity relation with a non-trivial exponent $\gamma_{cb}$ in a large intermediate regime. Our results offer a simple explanation for the large values of $\gamma_{cb}$ inferred from recent photoemission data from quasi one-dimensional conductors and might have some relevance for the understanding of the unusual properties of the high-temperature superconductors.Comment: compressed and uuencoded ps-file, including the figures, accepted for publication in Phys. Rev. Lett

Functional renormalization group approach to correlated fermion systems

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems, (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals, (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and non-equilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. We present a self-contained derivation of the exact flow equations and describe frequently used truncation schemes. Reviewing selected applications we then show how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.Comment: Review article, final version, 59 pages, 28 figure

Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation

We use our recently developed functional bosonization approach to bosonize interacting fermions in arbitrary dimension $d$ beyond the Gaussian approximation. Even in $d=1$ the finite curvature of the energy dispersion at the Fermi surface gives rise to interactions between the bosons. In higher dimensions scattering processes describing momentum transfer between different patches on the Fermi surface (around-the-corner processes) are an additional source for corrections to the Gaussian approximation. We derive an explicit expression for the leading correction to the bosonized Hamiltonian and the irreducible self-energy of the bosonic propagator that takes the finite curvature as well as around-the-corner processes into account. In the special case that around-the-corner scattering is negligible, we show that the self-energy correction to the Gaussian propagator is negligible if the dimensionless quantities $( \frac{q_{c} }{ k_{F}} )^d F_{0} [ 1 + F_{0} ]^{-1} \frac{\mu}{\nu^{\alpha}} | \frac{ \partial \nu^{\alpha} }{ \partial \mu} |$ are small compared with unity for all patches $\alpha$. Here $q_{c}$ is the cutoff of the interaction in wave-vector space, $k_{F}$ is the Fermi wave-vector, $\mu$ is the chemical potential, $F_{0}$ is the usual dimensionless Landau interaction-parameter, and $\nu^{\alpha}$ is the {\it{local}} density of states associated with patch $\alpha$. We also show that the well known cancellation between vertex- and self-energy corrections in one-dimensional systems, which is responsible for the fact that the random-phase approximation for the density-density correlation function is exact in $d=1$, exists also in $d> 1$, provided (1) the interaction cutoff $q_{c}$ is small compared with $k_{F}$, and (2) the energy dispersion is locally linearized at the Fermi the Fermi surface. Finally, we suggest a new systematic method to calculate corrections to the RPA, which is based on the perturbative calculation of the irreducible bosonic self-energy arising from the non-Gaussian terms of the bosonized Hamiltonian.Comment: The abstract has been rewritten. No major changes in the text