# A Single Impurity in a Luttinger Liquid: How It “Cuts” the Chain

@article{Meden2001ASI, title={A Single Impurity in a Luttinger Liquid: How It “Cuts” the Chain}, author={V Meden and Walter Metzner and Ulrich Schollw{\"o}ck and Kurt Sch{\"o}nhammer}, journal={Journal of Low Temperature Physics}, year={2001}, volume={126}, pages={1147-1163} }

Using a fermionic renormalization group method we present a simple real space picture of the strong influence an impurity has on the electronic properties of a Luttinger liquid. We compute the flow of the renormalized impurity potential for a single impurity over the entire energy range - from the microscopic scale of a lattice-fermion model down to the low-energy limit. We confirm that low energy properties close to the impurity are as if the chain is cut in two pieces with open boundary…

## 29 Citations

Renormalization group analysis of the one-dimensional extended Hubbard model with a single impurity

- Physics
- 2006

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…

Functional renormalization group analysis of Luttinger liquids with impurities

- Physics
- 2006

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…

Impurity and correlation effects on transport in one-dimensional quantum wires

- Physics
- 2005

We study transport through a one-dimensional quantum wire of correlated fermions connected to semi-infinite leads. The wire contains either a single impurity or two barriers, the latter allowing for…

Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids

- Physics
- 2008

We compare two fermionic renormalization group (RG) methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger…

Transport of interacting electrons through a double barrier in quantum wires

- Physics
- 2003

We generalize the fermionic renormalization group method to analytically describe transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting…

Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors

- Physics
- 2004

As a model of thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar…

Regular networks of Luttinger liquids

- Physics
- 2005

We consider arrays of Luttinger liquids, where each node is described by a unitary scattering matrix. In the limit of small electron-electron interaction, we study the evolution of these scattering…

Flow of the quasiparticle weight in the N-patch renormalization group scheme

- Physics
- 2003

Using the N-patch renormalization group method we investigate the flow of the quasiparticle weight in one-dimensional, weakly two-dimensional, and fully two-dimensional Hubbard models. In one…

Persistent currents in mesoscopic rings: A numerical and renormalization group study

- Physics
- 2003

The persistent current in a lattice model of a one-dimensional interacting electron system is systematically studied using a complex version of the density-matrix renormalization group algorithm and…

Universality at work – the local sine-Gordon model, lattice fermions, and quantum circuits

- PhysicsThe European Physical Journal Special Topics
- 2020

We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying…

## References

SHOWING 1-10 OF 39 REFERENCES

Weakly correlated electrons on a square lattice: Renormalization-group theory

- Physics
- 2000

We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in the form…

One-dimensional Fermi liquids

- Physics
- 1995

We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in…

Orthogonality catastrophe in a one-dimensional system of correlated electrons

- Physics
- 1998

We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix…

Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains.

- PhysicsPhysical review. B, Condensed matter
- 1992

We study the effect of an isolated impurity on the low-energy properties of a half-odd-integer-spin Heisenberg antiferromagnetic chin using both numerical and conformal field theory techniques. The…

Exact conductance through point contacts in the nu =1/3 fractional quantum Hall Effect.

- PhysicsPhysical review letters
- 1995

The conductance for tunneling through an impurity in a Luttinger liquid is described by a universal scaling function that is derived exactly, by using the thermodynamic Bethe ansatz and a kinetic (Boltzmann) equation.

Friedel oscillations for interacting fermions in one dimension.

- PhysicsPhysical review letters
- 1995

Friedel oscillations in one-dimensional electron liquid for arbitrary electron-electron interaction and arbitrary impurity strength are studied and a slower decay is found at intermediate distances from the impurity, with a crossover to the asymptotic x-g law.

Conduction of a weakly interacting one-dimensional electron gas through a single barrier.

- PhysicsPhysical review. B, Condensed matter
- 1994

Poor man's renormalization group procedure allows us to calculate the renormalized transmission amplitudes at any energies and simple formulas that describe the conductance at any temperature are derived.

Spin and interaction effects on charge distribution and currents in one-dimensional conductors and rings within the Hartree-Fock approximation.

- Physics
- 1998

Using the self-consistent Hartree-Fock approximation for electrons with spin at zero temperature, we study the effect of the electronic interactions on the charge distribution in a one- dimensional…

Spin- and charge-density oscillations in spin chains and quantum wires

- Physics
- 2000

We analyze the spin- and charge-density oscillations near impurities in spin chains and quantum wires. These so-called Friedel oscillations give detailed information about the impurity and also about…

New wave‐operator identity applied to the study of persistent currents in 1D

- Physics
- 1974

We show that a large class of backward‐scattering matrix elements involving Δk ∼ ± 2kF vanish for fermions interacting with two‐body attractive forces in one dimension. (These same matrix elements…