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:0803.2971 · Physical Review Letters

Transport in a Dissipative Luttinger Liquid

Zoran Ristivojević, Thomas Nattermann

Published Jul 3, 2008• 13 citations
arXivHTMLPDF

Abstract

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is $I\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{E}_{0}/eV)$, where ${E}_{0}\ensuremath{\sim}\ensuremath{\eta}/\ensuremath{\kappa}$ and $\ensuremath{\kappa}$ denotes the compressibility. At nonzero temperature $T$, the linear conductance is proportional to $\mathrm{exp}(\ensuremath{-}\sqrt{\mathcal{C}{E}_{0}/{k}_{B}T})$. The decay of Friedel oscillation saturates for a distance larger than ${L}_{\ensuremath{\eta}}\ensuremath{\sim}1/\ensuremath{\eta}$ from the impurity.

DOI
10.1103/physrevlett.101.016405

Related papers

Transport in a Luttinger liquid with dissipation: Two impurities

Leiming Chen, Zoran Ristivojević, Thomas Nattermann

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter $K$, and the deviation from the resonance condition is obtained. For weak dissipation and $1/2<K<1$, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.

arXiv:0906.3995•Physical Review B•Nov 2, 2009•0 citations

Transport in a one-channel Luttinger liquid

C. L. Kane, Matthew P. A. Fisher

We study theoretically the transport of a one-channel Luttinger liquid through a weak link. For repulsive electron interactions, the electrons are completely reflected by even the smallest scatterer, leading to a truly insulating weak link, in striking contrast to that for noninteracting electrons. At finite temperature (T) the conductance is nonzero, and is predicted to vanish as a power of T. At T=0 power-law current-voltage characteristics are predicted. For attractive interactions, a Luttinger liquid is argued to be perfectly transmitted through even the largest of barriers. The role of Fermi-liquid leads is also explored.

Physical Review Letters•Feb 24, 1992•1,131 citations

Impurity-induced coherent current oscillations in one-dimensional conductors

Sergey N. Artemenko, S. V. Remizov, D. S. Shapiro

The electronic transport through a single impurity in a repulsive Luttinger liquid (LL) has been theoretically studied. It has been found that the direct current Ī above the threshold voltage related to the strength of the impurity potential is accompanied by coherent oscillations with frequency f = Ī / e . There is an analogy with the Josephson junctions: the well-known regime of the power-law I − V curves in the LL corresponds to the damping of the Josephson current below the critical one, while the oscillatory regime in the LL can be compared with the Josephson oscillations above the critical current.

arXiv:0804.4113•Journal of Experimental and Theoretical Physics Letters•Aug 1, 2008•3 citations

Dissipative Luttinger liquids

Aaron J. Friedman

We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, $ρ$. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature $T>0$. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.

arXiv:1910.06371•Oct 14, 2019•2 citations

Thermal Transport in a Luttinger Liquid

C. L. Kane, Matthew P. A. Fisher

We study thermal transport in a one-dimensional (1D) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1D gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi liquid---the Wiedemann-Franz law---is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by $L(T\ensuremath{\rightarrow}0){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3L}_{0}/({2g+g}^{2})$---with ${L}_{0}$ the Fermi liquid value---and the conductance $1/2<g<1$. For $g<1/2$ the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.

arXiv:cond-mat/9509068•Physical Review Letters•Apr 22, 1996•194 citations

Bath-induced phase transition in a Luttinger liquid

Saptarshi Majumdar, Laura Foini, Thierry Giamarchi +1 more

We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by a Kosterlitz-Thouless transition. At low coupling with the bath, the chain remains in a Luttinger liquid (LL) phase with a reduced but finite spin stiffness, while above a critical coupling, the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: The LL is a perfect conductor, while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder-inducing signatures of localization.

arXiv:2210.01590•Physical review. B./Physical review. B•Apr 7, 2023•9 citations
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is I\ensuremath∼exp(\ensuremath−E0/eV)I\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{E}_{0}/eV)I\ensuremath∼exp(\ensuremath−E0​/eV), where E0\ensuremath∼\ensuremathη/\ensuremathκ{E}_{0}\ensuremath{\sim}\ensuremath{\eta}/\ensuremath{\kappa}E0​\ensuremath∼\ensuremathη/\ensuremathκ and \ensuremathκ\ensuremath{\kappa}\ensuremathκ denotes the compressibility. At nonzero temperature TTT, the linear conductance is proportional to exp(\ensuremath−CE0/kBT)\mathrm{exp}(\ensuremath{-}\sqrt{\mathcal{C}{E}_{0}/{k}_{B}T})exp(\ensuremath−CE0​/kB​T​). The decay of Friedel oscillation saturates for a distance larger than L\ensuremathη\ensuremath∼1/\ensuremathη{L}_{\ensuremath{\eta}}\ensuremath{\sim}1/\ensuremath{\eta}L\ensuremathη​\ensuremath∼1/\ensuremathη from the impurity.
We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter KKK, and the deviation from the resonance condition is obtained. For weak dissipation and 1/2<K<11/2<K<11/2<K<1, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.
We study theoretically the transport of a one-channel Luttinger liquid through a weak link. For repulsive electron interactions, the electrons are completely reflected by even the smallest scatterer, leading to a truly insulating weak link, in striking contrast to that for noninteracting electrons. At finite temperature (T) the conductance is nonzero, and is predicted to vanish as a power of T. At T=0 power-law current-voltage characteristics are predicted. For attractive interactions, a Luttinger liquid is argued to be perfectly transmitted through even the largest of barriers. The role of Fermi-liquid leads is also explored.
The electronic transport through a single impurity in a repulsive Luttinger liquid (LL) has been theoretically studied. It has been found that the direct current Ī above the threshold voltage related to the strength of the impurity potential is accompanied by coherent oscillations with frequency f = Ī / e . There is an analogy with the Josephson junctions: the well-known regime of the power-law I − V curves in the LL corresponds to the damping of the Josephson current below the critical one, while the oscillatory regime in the LL can be compared with the Josephson oscillations above the critical current.
We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, ρρρ. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature T>0T>0T>0. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.
We study thermal transport in a one-dimensional (1D) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1D gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi liquid---the Wiedemann-Franz law---is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by $L(T\ensuremath{\rightarrow}0){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3L}_{0}/({2g+g}^{2})$---with L0{L}_{0}L0​ the Fermi liquid value---and the conductance 1/2<g<11/2<g<11/2<g<1. For g<1/2g<1/2g<1/2 the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.
We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by a Kosterlitz-Thouless transition. At low coupling with the bath, the chain remains in a Luttinger liquid (LL) phase with a reduced but finite spin stiffness, while above a critical coupling, the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: The LL is a perfect conductor, while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder-inducing signatures of localization.