152 research outputs found
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 and the dimensionless frequency dependent conductance for quantum spin models. It is shown that spin diffusion implies the
vanishing of the Drude peak of , and that the spin diffusion
coefficient is proportional to . We develop a new method based on
the Thouless number to calculate , and present results for in the
nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for
arbitrary dimension and spin .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.
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
Functional Bosonization of Interacting Fermions in Arbitrary Dimensions
We bosonize the long-wavelength excitations of interacting fermions in
arbitrary dimension by directly applying a suitable Hubbard-Stratonowich
transformation to the Grassmannian generating functional of the fermionic
correlation functions. With this technique we derive a surprisingly simple
expression for the single-particle Greens-function, which is valid for
arbitrary interaction strength and can describe Fermi- as well as Luttinger
liquids. Our approach sheds further light on the relation between bosonization
and the random-phase approximation, and enables us to study screening in a
non-perturbative way.Comment: Revtex; no figure
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
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