Functional Renormalization-Group Analysis of Luttinger Liquids with Impurities
arXiv:cond-mat/0603341 · doi:10.18419/opus-6599
Abstract
In one-dimensional quantum wires the interplay of electron correlations and impurities strongly influences the low-energy physics. The diversity of energy scales and the competition of correlations in interacting Fermi systems can be treated very efficiently with the functional renormalization group (fRG), describing the gradual evolution from a microscopic model Hamiltonian to the effective low-energy action as a function of a continuously decreasing energy cutoff. The fRG provides the universal low-energy asymptotics as well as nonuniversal properties, and in particular an answer to the important question at what scale the ultimate asymptotics sets in. We investigate the influence of impurities on spectral and transport properties of fermionic lattice models with short-range interactions. The results capture relevant energy scales and crossover phenomena, in addition to the universal low-energy asymptotics. For weak and intermediate impurity strengths the asymptotic behavior is approached only at rather low energy scales, accessible only for very large systems. For spin-1/2 systems 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.
PhD thesis; http://elib.uni-stuttgart.de/opus/volltexte/2006/2534/
References in corpus (18)
- The temperature-flow renormalization group and the competition between superconductivity and ferromagnetism
- Resonant tunneling of interacting electrons in a one-dimensional wire
- Tomonaga-Luttinger parameters for doped Mott insulators
- Interaction flow method for many-fermion systems
- Transport of interacting electrons through a double barrier in quantum wires
- Functional renormalization group for Luttinger liquids with impurities
- Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
- Functional Renormalization Group Analysis of the Half-filled One-dimensional Extended Hubbard Model
- Transmission Probability for Interacting Electrons Connected to Reservoirs
- Competing phases in the extended U-V-J Hubbard model near the van Hove fillings: 2-patch approach
- Competing phases in the extended U-V-J Hubbard model near the van Hove fillings
- The conductance of interacting nano-wires
- Persistent currents in mesoscopic rings: A numerical and renormalization group study
- Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
- Scaling behavior of impurities in mesoscopic Luttinger liquids
- Correlation effects on resonant tunneling in one-dimensional quantum wires
- Scaling of the conductance in a quantum wire
- Kondo physics in transport through a quantum dot with Luttinger liquid leads