• Open Access

Two-wire junction of inequivalent Tomonaga-Luttinger liquids

Yao-Tai Kang, Chung-Yu Lo, Masaki Oshikawa, Ying-Jer Kao, and Pochung Chen
Phys. Rev. B 104, 235142 – Published 22 December 2021

Abstract

We develop two numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a voltage bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infinite-size matrix product state to minimize the finite-size effects. Due to the lack of the translational invariance, we focus on a finite-size window containing the junction. For time-independent calculations, we use infinite boundary conditions to evaluate the correlations within the window. For time-dependent calculations, we use the window technique to evaluate the local currents within the window. The numerical results obtained by both schemes show excellent agreement with the analytical predictions.

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  • Received 19 May 2021
  • Revised 8 December 2021
  • Accepted 8 December 2021

DOI:https://doi.org/10.1103/PhysRevB.104.235142

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yao-Tai Kang1,2, Chung-Yu Lo2, Masaki Oshikawa3, Ying-Jer Kao4,5,*, and Pochung Chen2,5,6,†

  • 1School of Electronic and Electrical Engineering, Zhaoqing University, Zhaoqing 526061, China
  • 2Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
  • 3Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
  • 4Department of Physics, National Taiwan University, Taipei 10607, Taiwan
  • 5Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
  • 6Frontier Center for Theory and Computation, National Tsing Hua University, Hsinchu 30013, Taiwan

  • *yjkao@phys.ntu.edu.tw
  • pcchen@phys.nthu.edu.tw

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Issue

Vol. 104, Iss. 23 — 15 December 2021

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