The weak localization correction to the polarization and persistent currents in mesoscopic metal rings

We re-examine the effect of electron-electron interactions on the persistent current in mesoscopic metal rings threaded by an Aharonov-Bohm flux. The exchange contribution to the current is shown to be determined by the weak localization correction to the polarization. We explicitly calculate the contribution from exchange interactions with momentum transfers smaller than the inverse elastic mean free path to the average current, and find that it has the same order of magnitude as the {\it{canonical}} current without interactions. \\Comment: additional vertex correction taken into account: weak localization correction to the diffusion coefficient in the denominator changes final resul

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.

Effective average action based approach to correlation functions at finite momenta

We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion which includes both all local correlations and two-point and four-point irreducible correlations to all orders in the derivatives. We discuss schemes for both the symmetric and the symmetry broken phase of the O(N) model and present results for D=3. All approximations are done directly in the effective average action rather than in the flow equations of irreducible vertices. The approach is numerically relatively easy to implement and yields good results for all N both for the critical exponents as well as for the momentum dependence of the two-point function.Comment: 6 pages, 1 figure, 3 table

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