Relaxation in Luttinger liquids: Bose-Fermi duality

I. V. Protopopov, D. B. Gutman, A. D. Mirlin

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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 λ=m∗l2T and the bosonic theory by λ-1, where 1/m∗ and l characterize the curvature of the fermionic and bosonic spectra, respectively, and T is the temperature.

Original languageEnglish
Article number125113
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number12
StatePublished - 8 Sep 2014

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© 2014 American Physical Society.


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