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/9901032 · Physical review. B, Condensed matter

Universal behavior of quantum impurity scattering in a Tomonaga-Luttinger liquid

Yu-Liang Liu

Published Mar 15, 1999• 8 citations
arXivHTMLPDF

Abstract

Using bosonization and path-integral methods, we study general low-temperature behavior of nonmagnetic and magnetic impurity scattering in Tomonaga-Luttinger liquid, and calculate the electron Green function for a general backward scattering potential. We demonstrate that the electron density of state near the impurity site is suppressed by backward scattering, but it mainly remains invariant far away from the impurity, and that at zero temperature the electrons are completely reflected on the impurity site; the system breaks into two subsystems, but right- and left-moving electron fields have a twisted boundary condition. We also show that a testing charge can only be partially screened by conduction electrons, and in a strong interaction region the impurity susceptibility has a $1/T$-type low-temperature behavior.

DOI
10.1103/physrevb.59.7937

Related papers

Numerical study of transport through a single impurity in a spinful Tomonaga–Luttinger liquid

Yuji Hamamoto, Ken‐Ichiro Imura, Takeo Kato

The single impurity problem in a spinful Tomonaga--Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the nonperturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either perfect transmission or reflection of charge and spin channels. Our phase diagram for an intermediate scattering strength is consistent with the standard perturbative renormalization group (RG) analysis in the limit of weak and strong backward scatterings, in the sense that all our phase boundaries interpolate the two limiting cases. Further investigations show, however, that precise location and form of our phase boundaries are not trivially explained by the standard RG analysis, e.g., some part of the phase diagram looks much similar to the weak backscattering limit, whereas some other part is clearly derived from the opposite limit. In order to give a more intuitive interpretation of such behaviors, we also reconsidered our impurity problem from the viewpoint of a quantum Brownian motion picture.

arXiv:0710.3474•Physical Review B•Apr 2, 2008•17 citations

Low Temperature Behavior of the Kondo Effect in Tomonaga-Luttinger Liquid

Yu-Liang Liu

Using the bosonization method, we study the low temperature behavior of the Kondo effect in the Tomonaga-Luttinger liquid and clearly show that the power law temperature dependence of the impurity susceptibility is completely determined by the repulsive electron-electron interaction existing in the total spin channel and is independent of the electron-electron interaction existing in the charge channels.

arXiv:cond-mat/9710262•Oct 24, 1997•0 citations

Magnetic impurity in a Luttinger liquid: A conformal field theory approach

Per Fröjdh, Henrik Johannesson

We study the low-temperature properties of a spin-1/2 magnetic impurity coupled to a one-dimensional interacting electron system. Using a formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for noninteracting electrons, but with a different Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward and backward scattering (Kondo interaction), we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a critical theory with an anomalous specific heat. The latter case agrees with a recent poor-man's scaling result proposed by Furusaki and Nagaosa. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9506099•Physical review. B, Condensed matter•Feb 1, 1996•53 citations

Kondo effect in a Tomonaga-Luttinger liquid

Akira Furusaki, Naoto Nagaosa

The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.

Physical Review Letters•Feb 7, 1994•204 citations

Transport properties in the Tomonaga-Luttinger liquid

Masao Ogata, Philip Warren Anderson

We investigate the conductivity using Green's functions in the Tomonaga-Luttinger liquid. It is shown that the resistivity has a linear temperature dependence if we take account of the physical process that the accelerated electron decays into spinon and holon. The effect of impurity scattering becomes visible only below a crossover temperature which strongly depends on the impurity strength, energy cutoff, and spin and charge velocities. The optical conductivity is also studied and it is shown that the relaxation rate has a linear frequency dependence.

Physical Review Letters•May 17, 1993•59 citations

Local perturbation in a Tomonaga-Luttinger liquid at g=1/2: Orthogonality catastrophe, Fermi-edge singularity, and local density of states

Akira Furusaki

The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurity is reexamined for the case when the interaction parameter or the dimensionless conductance is $g=1/2.$ By transforming bosons back to fermions, the Hamiltonian is reduced to a quadratic form, which allows for explicit calculation of the overlap integral and the local density of states at the defect site. The exponent of the orthogonality catastrophe due to a backward scattering center is found to be 1/8, in agreement with previous studies using different approaches. The time dependence of the core-hole Green's function is computed numerically, which shows a clear crossover from a nonuniversal short-time behavior to a universal long-time behavior. The local density of states vanishes linearly in the low-energy limit at $g=1/2.$

arXiv:cond-mat/9702195•Physical review. B, Condensed matter•Oct 15, 1997•42 citations
Using bosonization and path-integral methods, we study general low-temperature behavior of nonmagnetic and magnetic impurity scattering in Tomonaga-Luttinger liquid, and calculate the electron Green function for a general backward scattering potential. We demonstrate that the electron density of state near the impurity site is suppressed by backward scattering, but it mainly remains invariant far away from the impurity, and that at zero temperature the electrons are completely reflected on the impurity site; the system breaks into two subsystems, but right- and left-moving electron fields have a twisted boundary condition. We also show that a testing charge can only be partially screened by conduction electrons, and in a strong interaction region the impurity susceptibility has a 1/T1/T1/T-type low-temperature behavior.
The single impurity problem in a spinful Tomonaga--Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the nonperturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either perfect transmission or reflection of charge and spin channels. Our phase diagram for an intermediate scattering strength is consistent with the standard perturbative renormalization group (RG) analysis in the limit of weak and strong backward scatterings, in the sense that all our phase boundaries interpolate the two limiting cases. Further investigations show, however, that precise location and form of our phase boundaries are not trivially explained by the standard RG analysis, e.g., some part of the phase diagram looks much similar to the weak backscattering limit, whereas some other part is clearly derived from the opposite limit. In order to give a more intuitive interpretation of such behaviors, we also reconsidered our impurity problem from the viewpoint of a quantum Brownian motion picture.
We study the low-temperature properties of a spin-1/2 magnetic impurity coupled to a one-dimensional interacting electron system. Using a formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for noninteracting electrons, but with a different Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward and backward scattering (Kondo interaction), we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a critical theory with an anomalous specific heat. The latter case agrees with a recent poor-man's scaling result proposed by Furusaki and Nagaosa. \textcopyright{} 1996 The American Physical Society.
The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.
We investigate the conductivity using Green's functions in the Tomonaga-Luttinger liquid. It is shown that the resistivity has a linear temperature dependence if we take account of the physical process that the accelerated electron decays into spinon and holon. The effect of impurity scattering becomes visible only below a crossover temperature which strongly depends on the impurity strength, energy cutoff, and spin and charge velocities. The optical conductivity is also studied and it is shown that the relaxation rate has a linear frequency dependence.
The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurity is reexamined for the case when the interaction parameter or the dimensionless conductance is g=1/2.g=1/2.g=1/2. By transforming bosons back to fermions, the Hamiltonian is reduced to a quadratic form, which allows for explicit calculation of the overlap integral and the local density of states at the defect site. The exponent of the orthogonality catastrophe due to a backward scattering center is found to be 1/8, in agreement with previous studies using different approaches. The time dependence of the core-hole Green's function is computed numerically, which shows a clear crossover from a nonuniversal short-time behavior to a universal long-time behavior. The local density of states vanishes linearly in the low-energy limit at g=1/2.g=1/2.g=1/2.