The Emergence of the Noninteracting Channel in the Strongly Interacting 1D System

Igor Valery Yurkevich, Victor Kagalovsky

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A strongly interacting 1D system with many channels is studied. When single-electron interchannel backscattering processes become relevant, new fields are defined. Some fields are frozen (gapped) by these relevant perturbations, whereas others remain free. A mathematical procedure to separate gapped and conducting channels is proposed. The problem for a two-channel system with particular relevant perturbation is then solved exactly for arbitrary intra- and interchannel interactions, and effective Luttinger parameter and velocity for the free field are found. The parameters of the free field are independent of the interactions between right- and left-moving electrons in the same channel and between electrons moving in the same direction in different channels. Finally, if the interchannel interactions are weak, the free field becomes noninteracting (effective Luttinger parameter (Formula presented.)) independently of how strong intrachannel interactions are.

Original languageEnglish
Article number2200485
Journalphysica status solidi (RRL) – Rapid Research Letters
Issue number11
Early online date13 Jan 2023
Publication statusPublished - Nov 2023

Bibliographical note

Copyright © 2023 The Authors. physica status solidi (RRL) Rapid Research Letters published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License [], which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Funding & Acknowledgements: The authors are grateful to M. Pepper for illuminating discussions. This work was supported by the Leverhulme Trust grant no. RPG-2019-317 (I.V.Y.), MOST/MESU grant no. 3-16430 (V.K.), and the SCE internal grant EXR01/Y17/T1/D3/Yr1 (V.K.). The authors are grateful for the hospitality extended to them at the Center for Theoretical Physics of Complex Systems, Daejeon, South Korea (I.V.Y. and V.K.), and at the SCE (I.V.Y.).


  • effective Luttinger parameters
  • relevant perturbations
  • strongly interacting 1D systems


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