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

Bulletin of the American Physical Society

Duality of Weak and Strong Scatterer in Luttinger Liquid Coupled to Massless Bosons

Alexey Galda, I. V. Yurkevich, Oleg M. Yevtushenko, Igor V. Lerner

Published Mar 20, 2013• 1 citation
OpenAlex

Related papers

Potential scattering in a Luttinger liquid: weak versus strong correlations

Debanand Sa

Solid State Communications•Dec 1, 1999•0 citations

Interacting resonant level side-coupled to a Luttinger liquid: Duality to resonant tunneling

Moshe Goldstein, Richard Berkovits

Bulletin of the American Physical Society•Mar 16, 2009•0 citations

Duality of Weak and Strong Scatterer in a Luttinger Liquid Coupled to Massless Bosons

I. V. Yurkevich, Alexey Galda, Oleg M. Yevtushenko +1 more

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ΔWSΔWL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

arXiv:1209.4788•Physical Review Letters•Mar 28, 2013•20 citations

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

Elmar Haller, Russell Hart, Manfred J. Mark +6 more

arXiv:1004.3168•Nature•Jul 1, 2010•255 citations

Universal duality in a Luttinger liquid coupled to a generic environment

I. V. Yurkevich, Oleg M. Yevtushenko

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

arXiv:1403.6357•Physical Review B•Sep 9, 2014•5 citations

Relaxation in Luttinger liquids: Bose-Fermi duality

Ivan V. Protopopov, Dmitri B. Gutman, A. D. Mirlin

We explore the lifetime of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant $\ensuremath{\lambda}={m}^{*}{l}^{2}T$ and the bosonic theory by ${\ensuremath{\lambda}}^{\ensuremath{-}1}$, where $1/{m}^{*}$ and $l$ characterize the curvature of the fermionic and bosonic spectra, respectively, and $T$ is the temperature.

arXiv:1404.0178•Physical Review B•Sep 8, 2014•29 citations
We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ΔWSΔWL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.
We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.
We explore the lifetime of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant $\ensuremath{\lambda}={m}^{*}{l}^{2}T$ and the bosonic theory by ${\ensuremath{\lambda}}^{\ensuremath{-}1}$, where 1/m∗1/{m}^{*}1/m∗ and lll characterize the curvature of the fermionic and bosonic spectra, respectively, and TTT is the temperature.