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Metal-insulator transition in a boundary three chain model

Niels John1,*, Yuval Gefen2, and Bernd Rosenow1,†

  • *Deceased.
  • †Contact author: rosenow@physik.uni-leipzig.de
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Phys. Rev. B 113, 035156 – Published 29 January, 2026

DOI: https://doi.org/10.1103/rq6s-z87r

Abstract

We study the boundary physics of topologially trivial Mott insulators, representing the boundary by three coupled Hubbard chains in a linear confining potential. In the Hartree-Fock approximation, the ground state at and slightly off the particle-hole symmetric point remains insulating even at large slopes of the confining potential. By contrast, accounting for quantum fluctuations and correlations through a combination of bosonization and renormalization group (RG) methods, we find that there is always a gapless dipole mode, but it does not contribute to a finite compressibility. Moreover, when increasing the slope of the confining potential at half filling, we find a quantum phase transition between an insulating and a metallic state, indicating the formation of a soft edge state of non-topological origin. Away from half filling, a similar transition takes place.

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References (27)

  1. B. I. Halperin, Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B 25, 2185 (1982).
  2. R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632 (1981).
  3. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  4. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  5. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  6. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  7. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007).
  8. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  9. X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press, Oxford, 2007).
  10. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005).
  11. J. M. Kosterlitz and D. J. Thouless, Long range order and metastability in two dimensional solids and superfluids (Application of dislocation theory), J. Phys. C 5, L124 (1972).
  12. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6, 1181 (1973).
  13. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  14. N. F. Mott, The basis of the electron theory of metals, with special reference to the transition metals, Proc. Phys. Soc. Lond. Sect. A 62, 416 (1949).
  15. H. J. Schulz, in Strongly Correlated Magnetic and Superconducting Systems, edited by G. Sierra and M. A. Martín-Delgado (Springer-Verlag, Berlin, Heidelberg, 1997), pp. 136–136.
  16. L. Balents and M. P. A. Fisher, Weak-coupling phase diagram of the two-chain Hubbard model, Phys. Rev. B 53, 12133 (1996).
  17. K. L. Hur, Critical Ising modes in low-dimensional Kondo insulators, Phys. Rev. B 63, 165110 (2001).
  18. T. Giamarchi and O. U. Press, Quantum Physics in One Dimension, International Series of Monographs (Clarendon Press, Oxford, 2004).
  19. A. M. Finkel'stein and A. I. Larkin, Conductance fluctuations in one-dimensional systems, Phys. Rev. B 47, 10461 (1993).
  20. J.-J. Miao, F.-C. Zhang, and Y. Zhou, Instability of three-band Tomonaga-Luttinger liquid: Renormalization group analysis and possible application to K2Cr3As3, Phys. Rev. B 94, 205129 (2016).
  21. M. Tsuchiizu, P. Donohue, Y. Suzumura, and T. Giamarchi, Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons, Eur. Phys. J. B 19, 185 (2001).
  22. U. Khanna, Y. Gefen, O. Entin-Wohlman, and A. Aharony, Edge reconstruction of a time-reversal invariant insulator: Compressible-incompressible stripes, Phys. Rev. Lett. 128, 186801 (2022).
  23. J. von Delft and H. Schoeller, Bosonization for beginners – refermionization for experts, Ann. Phys. 510, 225 (1998).
  24. Note that in principle one should consider the renormalization of the Kρ(γ) due to the umklapp couplings appearing in Hint2kF [18]. However, even when only renormalizing the g3(γ), one still obtains the qualitatively correct answer regarding their relevance or irrelevance, which only depends on the signum of the initial value of 2−2Kρ(γ) [18]. Thus, on a qualitative level the answer regarding the relevance of the g3(γ) is not changed if we neglect the renormalization of the Kρ(γ).
  25. B. Rosenow and B. I. Halperin, Nonuniversal behavior of scattering between fractional quantum Hall edges, Phys. Rev. Lett. 88, 096404 (2002).
  26. J. Li, R.-X. Zhang, Z. Yin, J. Zhang, K. Watanabe, T. Taniguchi, C. Liu, and J. Zhu, A valley valve and electron beam splitter, Science 362, 1149 (2018).
  27. H. Overweg, H. Eggimann, X. Chen, S. Slizovskiy, M. Eich, R. Pisoni, Y. Lee, P. Rickhaus, K. Watanabe, T. Taniguchi, V. Fal'ko, T. Ihn, and K. Ensslin, Electrostatically induced quantum point contacts in bilayer graphene, Nano Lett. 18, 553 (2018).

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Phys. Rev. B 113, 035156– Published 29 January, 2026
  • Received 15 February 2022
  • Revised 21 July 2022
  • Accepted 18 November 2025
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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.

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