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Abstract:
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.
