Bosonization and the eikonal expansion: similarities and differences

We compare two non-perturbative techniques for calculating the single-particle Green's function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green's function is first calculated for a fixed configuration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the quasi-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green's function predicted by the eikonal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behavior of the spectral function, nor predicts the correct location of its singularities.Comment: Revtex, one figur

Thouless number and spin diffusion in quantum Heisenberg ferromagnets

Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number $g_0$ and the dimensionless frequency dependent conductance $g( \omega )$ for quantum spin models. It is shown that spin diffusion implies the vanishing of the Drude peak of $g ( \omega )$, and that the spin diffusion coefficient $D_s$ is proportional to $g_0$. We develop a new method based on the Thouless number to calculate $D_s$, and present results for $D_s$ in the nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for arbitrary dimension $d$ and spin $S$.Comment: 13 pages, written in latex MPLA2.sty (latex style distributed by International Journal of Modern Physics, the style file is given at the beginning, so just run latex

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green's function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is {\it{not}} based on the assumption that the electronic system is a Fermi liquid. For isotropic three-dimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure {\it{or in the phonon frequencies}}.Comment: I have added a few lines to show how the Bohm-Staver relation can be derived within my approach. To appear in Z. Phys.

Vertex corrections in gauge theories for two-dimensional condensed matter systems

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1 / q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative correction to the fermion - gauge field vertex leads to Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ], where a_{\eta} is a positive numerical constant and omega_0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent gamma to larger values.Comment: 6 figure

Spectral correlations in disordered mesoscopic metals and their relevance for persistent currents

We use the Lanczos method to calculate the variance of the number of energy levels in an energy window of width E below the Fermi energy for non-interacting disordered electrons on a thin three-dimensional ring threaded by an Aharonov-Bohm flux . We find that for small E the flux-dependent part of the variance is well described by a well-known Feynman diagram involving two Cooperons. However, this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents.Comment: minor modifications in the text, accepted for publication in Mod. Phys. Lett.

Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap Delta (x) that is constrained to be of the form Delta (x) = A e^{i Q x}, where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. {\bf{31}}, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of Delta (x) vanishes and its covariance is < Delta (x) Delta^{*} (x^{prime}) > = Delta_s^2 exp[ {- | x - x^{\prime} | / \xi}], we study the combined effect of phase and amplitude fluctutations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singulatity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors.Comment: 19 pages, 8 figures, submitted to European Physical Journal