7 research outputs found
Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
We analyze the one-dimensional extended Hubbard model with a single static
impurity by using a computational technique based on the functional
renormalization group. This extends previous work for spinless fermions to
spin-1/2 fermions. The underlying approximations are devised for weak
interactions and arbitrary impurity strengths, and have been checked by
comparing with density-matrix renormalization-group data. We present results
for the density of states, the density profile and the linear conductance.
Two-particle backscattering leads to striking effects, which are not captured
if the bulk system is approximated by its low-energy fixed point, the Luttinger
model. In particular, the expected decrease of spectral weight near the
impurity and of the conductance at low energy scales is often preceded by a
pronounced increase, and the asymptotic power laws are modified by logarithmic
corrections.Comment: 36 pages, 13 figures, revised version as publishe
Functional renormalization group approach to zero-dimensional interacting systems
We apply the functional renormalization group method to the calculation of
dynamical properties of zero-dimensional interacting quantum systems. As case
studies we discuss the anharmonic oscillator and the single impurity Anderson
model. We truncate the hierarchy of flow equations such that the results are at
least correct up to second order perturbation theory in the coupling. For the
anharmonic oscillator energies and spectra obtained within two different
functional renormalization group schemes are compared to numerically exact
results, perturbation theory, and the mean field approximation. Even at large
coupling the results obtained using the functional renormalization group agree
quite well with the numerical exact solution. The better of the two schemes is
used to calculate spectra of the single impurity Anderson model, which then are
compared to the results of perturbation theory and the numerical
renormalization group. For small to intermediate couplings the functional
renormalization group gives results which are close to the ones obtained using
the very accurate numerical renormalization group method. In particulare the
low-energy scale (Kondo temperature) extracted from the functional
renormalization group results shows the expected behavior.Comment: 22 pages, 8 figures include
Functional renormalization group for Luttinger liquids with impurities
We improve the recently developed functional renormalization group (fRG) for
impurities and boundaries in Luttinger liquids by including renormalization of
the two-particle interaction, in addition to renormalization of the impurity
potential. Explicit flow-equations are derived for spinless lattice fermions
with nearest neighbor interaction at zero temperature, and a fast algorithm for
solving these equations for very large systems is presented. We compute
spectral properties of single-particle excitations, and the oscillations in the
density profile induced by impurities or boundaries for chains with up to
1000000 lattice sites. The expected asymptotic power-laws at low energy or long
distance are fully captured by the fRG. Results on the relevant energy scales
and crossover phenomena at intermediate scales are also obtained. A comparison
with numerical density matrix renormalization results for systems with up to
1000 sites shows that the fRG with the inclusion of vertex renormalization is
remarkably accurate even for intermediate interaction strengths.Comment: 35 pages, 16 figures, revised version as publishe