Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9705269 · Physical review. B, Condensed matter

Impurity in a Luttinger liquid away from half-filling: A numerical study

Shaojin Qin, Michele Fabrizio, Lu Yu, Masaki Oshikawa, Ian K. Affleck

Published Oct 15, 1997• 49 citations
arXivHTMLPDF

Abstract

Conformal field theory gives quite detailed predictions for the low-energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was until now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density-matrix renormalization-group technique. Our results confirm conformal-field-theory predictions, and suggest that they are indeed valid for arbitrary fillings.

DOI
10.1103/physrevb.56.9766

Related papers

Impurity in a Luttinger liquid: A numerical study of the finite-size energy spectrum and of the orthogonality catastrophe exponent

Shaojin Qin, Michele Fabrizio, Lu Yu

The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density-matrix renormalization group. By analyzing the finite-size scaling behavior of the low-energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction.

arXiv:cond-mat/9608024•Physical review. B, Condensed matter•Oct 1, 1996•33 citations

A single impurity in a Luttinger liquid: How it

V. Meden, Walter Metzner, Ulrich Schollwoeck +1 more

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 conditions at the end points, but show that this universal behavior is only reached for extremely large systems. The accuracy of the renormalization group scheme is demonstrated by a direct comparison with data obtained from the density-matrix renormalization group method.

•Sep 2, 2001•0 citations

DMRG Studies of Impurities in Luttinger Liquids

U. Schollwöck, V. Meden, Walter Metzner +1 more

Using the Density Matrix Renormalization Group (DMRG) and various analytical techniques (functional renormalization) we consider the effects of local impurities in Luttinger liquids. We find that the universal physics predicted by bosonization sets in only at extremely long, experimentally arguably irrelevant length scales or small energy scales respectively. The explicit construction of the RG flow allows to trace this behaviour to an extremely weak renormalization in real space of the impurities associated to the generation of a very long-ranged oscillating scattering potential.

Progress of Theoretical Physics Supplement•Jan 1, 2002•3 citations

Impurity in a Luttinger liquid away from half-filling : a numerical study

Masaki Oshikawa

•Jan 1, 1997•0 citations

Critical behavior of Tomonaga-Luttinger liquids with a mobile impurity

Yasumasa Tsukamoto, Tatsuya Fujii, Norio Kawakami

The critical properties of Tomonaga-Luttinger liquids including a mobile impurity are studied by means of the Bethe ansatz method, conformal field theory (CFT), and bosonization. We calculate conformal dimensions by performing the CFT analysis of the energy spectrum for an integrable impurity model, and show that this system is classified as $c=1$ shifted Gaussian CFT. The exact critical exponents of various correlation functions are obtained as functions of the impurity mass and its momentum. Passing to the continuum limit, we then construct an effective field theory in terms of bosonization, and directly calculate some correlation functions. A possible application to the Fermi-edge singularity in quantum wires is also discussed.

Physical review. B, Condensed matter•Aug 15, 1998•36 citations

Conformal-field-theory approach to the two-impurity Kondo problem: Comparison with numerical renormalization-group results

Ian K. Affleck, Andreas W. W. Ludwig, Barbara Jones

Numerical renormalization-group and conformal-field-theory work indicate that the two-impurity Kondo Hamiltonian has a non-Fermi-liquid critical point separating the Kondo-screening phase from the interimpurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurrence of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyze this critical point using the boundary conformal-field-theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behavior, and a hidden SO(7) are analyzed.

arXiv:cond-mat/9409100•Physical review. B, Condensed matter•Oct 1, 1995•246 citations
Conformal field theory gives quite detailed predictions for the low-energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was until now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density-matrix renormalization-group technique. Our results confirm conformal-field-theory predictions, and suggest that they are indeed valid for arbitrary fillings.
The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density-matrix renormalization group. By analyzing the finite-size scaling behavior of the low-energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction.
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 conditions at the end points, but show that this universal behavior is only reached for extremely large systems. The accuracy of the renormalization group scheme is demonstrated by a direct comparison with data obtained from the density-matrix renormalization group method.
Using the Density Matrix Renormalization Group (DMRG) and various analytical techniques (functional renormalization) we consider the effects of local impurities in Luttinger liquids. We find that the universal physics predicted by bosonization sets in only at extremely long, experimentally arguably irrelevant length scales or small energy scales respectively. The explicit construction of the RG flow allows to trace this behaviour to an extremely weak renormalization in real space of the impurities associated to the generation of a very long-ranged oscillating scattering potential.
The critical properties of Tomonaga-Luttinger liquids including a mobile impurity are studied by means of the Bethe ansatz method, conformal field theory (CFT), and bosonization. We calculate conformal dimensions by performing the CFT analysis of the energy spectrum for an integrable impurity model, and show that this system is classified as c=1c=1c=1 shifted Gaussian CFT. The exact critical exponents of various correlation functions are obtained as functions of the impurity mass and its momentum. Passing to the continuum limit, we then construct an effective field theory in terms of bosonization, and directly calculate some correlation functions. A possible application to the Fermi-edge singularity in quantum wires is also discussed.
Numerical renormalization-group and conformal-field-theory work indicate that the two-impurity Kondo Hamiltonian has a non-Fermi-liquid critical point separating the Kondo-screening phase from the interimpurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurrence of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyze this critical point using the boundary conformal-field-theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behavior, and a hidden SO(7) are analyzed.