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

Physical Review Letters

Local time-dependent perturbation in Luttinger liquid

Alexander O. Gogolin

Published Nov 1, 1993• 78 citations
Publisher

Abstract

The response of the Luttinger liquid to a local potential is studied at zero temperature. It exhibits a crossover behavior. On the largest time scale and in the case of repulsive electron-electron interaction, the backscattering from the potential contributes to the core-hole Green's function G(t) the factor (${\mathit{t}}_{0}$/t${)}^{1/8}$---a universal (potential independent) decay law. The orthogonality catastrophe remains of the same analytical type as for the simple metals.

DOI
10.1103/physrevlett.71.2995

Related papers

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

Fermi-edge singularity with backscattering in the Luttinger-liquid model

Nikolay V. Prokof'ev

We study the response of the interacting electron gas in one-dimension (1D) to a local external potential. In the low-frequency limit the power-law singularities are essentially modified by backscattering effects which, in the case of zero forward scattering, result in the universal critical exponent depending only on the Luttinger-liquid interactions. The results obtained may be used to describe singular responses of the 1D boson chains.

arXiv:cond-mat/9306040•Physical review. B, Condensed matter•Jan 15, 1994•54 citations

Singular responses of spin-incoherent Luttinger liquids

Gregory A. Fiete

Abstract. When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson’s orthogonality catastrophe and it is relevant for the so-called X-ray edge or Fermi edge singularity, and for tunneling into an interacting one dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: ωth ω−ωth) α Θ(ω − ωth) where ωth is a threshold frequency and α is an exponent characterizing the singular response. In this paper singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized, and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted. Singular responses of spin-incoherent Luttinger liquids 2 1.

•Dec 3, 2012•2 citations

Singular responses of spin-incoherent Luttinger liquids

Gregory A. Fiete

When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called x-ray edge or Fermi-edge singularity, and for tunneling into an interacting one-dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: [Formula: see text], where ω(th) is a threshold frequency and α is an exponent characterizing the singular response. In this review singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.

arXiv:0812.4452•Journal of Physics Condensed Matter•Apr 7, 2009•4 citations

Transport properties of a Luttinger liquid in the presence of several time-dependent impurities

D. Makogon, Vladimir Juričić, C. Morais Smith

We study the transport properties of a Luttinger liquid in the presence of several time-dependent weak pointlike impurities. Our starting point is the bosonized form of the Luttinger liquid Hamiltonian with a potential introduced by the impurities. We find the correction to the total current due to the backscattering of the electrons by the impurities in first order of perturbation theory for a general time-dependent impurity potential. We then apply this result to a single time-dependent impurity, and show that it reproduces the result obtained by Feldman and Gefen [Phys. Rev. B 67, 115337 (2003)], in particular that the current enhancement occurs only for strong repulsive electron-electron interactions. For the case of two impurities oscillating with the same frequency, we find that the dc component of the backscattering current is positive even for weak repulsive interactions, due to the presence of the interference term induced by spatial correlations in the Luttinger liquid. We show that the impurity frequencies at which the enhancement takes place form a bandlike structure. In the case of several impurities, the bands become broader, because of interference effects.

arXiv:cond-mat/0606148•Physical Review B•Oct 31, 2006•20 citations

Quench dynamics of the Tomonaga-Luttinger model with momentum-dependent interaction

Rentrop, J., Dirk Schuricht, V. Meden

We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.

•Jan 1, 2012•51 citations
The response of the Luttinger liquid to a local potential is studied at zero temperature. It exhibits a crossover behavior. On the largest time scale and in the case of repulsive electron-electron interaction, the backscattering from the potential contributes to the core-hole Green's function G(t) the factor (t0{\mathit{t}}_{0}t0​/t)1/8{)}^{1/8})1/8---a universal (potential independent) decay law. The orthogonality catastrophe remains of the same analytical type as for the simple metals.
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.
Abstract. When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson’s orthogonality catastrophe and it is relevant for the so-called X-ray edge or Fermi edge singularity, and for tunneling into an interacting one dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: ωth ω−ωth) α Θ(ω − ωth) where ωth is a threshold frequency and α is an exponent characterizing the singular response. In this paper singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized, and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted. Singular responses of spin-incoherent Luttinger liquids 2 1.
When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called x-ray edge or Fermi-edge singularity, and for tunneling into an interacting one-dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: [Formula: see text], where ω(th) is a threshold frequency and α is an exponent characterizing the singular response. In this review singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.
We study the transport properties of a Luttinger liquid in the presence of several time-dependent weak pointlike impurities. Our starting point is the bosonized form of the Luttinger liquid Hamiltonian with a potential introduced by the impurities. We find the correction to the total current due to the backscattering of the electrons by the impurities in first order of perturbation theory for a general time-dependent impurity potential. We then apply this result to a single time-dependent impurity, and show that it reproduces the result obtained by Feldman and Gefen [Phys. Rev. B 67, 115337 (2003)], in particular that the current enhancement occurs only for strong repulsive electron-electron interactions. For the case of two impurities oscillating with the same frequency, we find that the dc component of the backscattering current is positive even for weak repulsive interactions, due to the presence of the interference term induced by spatial correlations in the Luttinger liquid. We show that the impurity frequencies at which the enhancement takes place form a bandlike structure. In the case of several impurities, the bands become broader, because of interference effects.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.