Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators

Rodrigo G. Pereira1, Bruno F. Marquez2, Karen Hallberg2,3, Tim Bauer4,5, and Reinhold Egger6

Phys. Rev. B 113, 045402 – Published 2 January, 2026

DOI: https://doi.org/10.1103/wkmx-772j

Abstract

We study the tunneling density of states (TDOS) in one-dimensional (1D) Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. A. C. Hewson, The Kondo Problem to Heavy Fermions, Cambridge Studies in Magnetism (Cambridge University Press, Cambridge, 1993).
  2. Y. Chen, W.-Y. He, W. Ruan, J. Hwang, S. Tang, R. L. Lee, M. Wu, T. Zhu, C. Zhang, H. Ryu, F. Wang, S. G. Louie, Z.-X. Shen, S.-K. Mo, P. A. Lee, and M. F. Crommie, Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T−TaS2, Nat. Phys. 18, 1335 (2022).
  3. Q. Zhang, W.-Y. He, Y. Zhang, Y. Chen, L. Jia, Y. Hou, H. Ji, H. Yang, T. Zhang, L. Liu, H.-J. Gao, T. A. Jung, and Y. Wang, Quantum spin liquid signatures in monolayer 1T−NbSe2, Nat. Commun. 15, 2336 (2024).
  4. K. T. Law and P. A. Lee, 1T-TaS2 as a quantum spin liquid, Proc. Natl. Acad. Sci. USA 114, 6996 (2017).
  5. W.-Y. He, X. Y. Xu, G. Chen, K. T. Law, and P. A. Lee, Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T−TaS2, Phys. Rev. Lett. 121, 046401 (2018).
  6. A. Ribak, I. Silber, C. Baines, K. Chashka, Z. Salman, Y. Dagan, and A. Kanigel, Gapless excitations in the ground state of 1T−TaS2, Phys. Rev. B 96, 195131 (2017).
  7. M. Gomilšek, R. Žitko, M. Klanjšek, M. Pregelj, C. Baines, Y. Li, Q. M. Zhang, and A. Zorko, Kondo screening in a charge-insulating spinon metal, Nat. Phys. 15, 754 (2019).
  8. H. Murayama, Y. Sato, T. Taniguchi, R. Kurihara, X. Z. Xing, W. Huang, S. Kasahara, Y. Kasahara, I. Kimchi, M. Yoshida, Y. Iwasa, Y. Mizukami, T. Shibauchi, M. Konczykowski, and Y. Matsuda, Effect of quenched disorder on the quantum spin liquid state of the triangular-lattice antiferromagnet 1T−TaS2, Phys. Rev. Res. 2, 013099 (2020).
  9. H. Chen, F.-H. Wang, Q. Gao, X.-J. Gao, Z. Chen, Y. Huang, K. T. Law, X. Y. Xu, and P. Chen, Spectroscopic evidence for possible quantum spin liquid behavior in a two-dimensional Mott insulator, Phys. Rev. Lett. 134, 066402 (2025).
  10. G. Khaliullin and P. Fulde, Magnetic impurity in a system of correlated electrons, Phys. Rev. B 52, 9514 (1995).
  11. A. Kolezhuk, S. Sachdev, R. R. Biswas, and P. Chen, Theory of quantum impurities in spin liquids, Phys. Rev. B 74, 165114 (2006).
  12. S. Florens, L. Fritz, and M. Vojta, Kondo effect in bosonic spin liquids, Phys. Rev. Lett. 96, 036601 (2006).
  13. P. Ribeiro and P. A. Lee, Magnetic impurity in a U(1) spin liquid with a spinon Fermi surface, Phys. Rev. B 83, 235119 (2011).
  14. X.-M. Zheng and M. Kargarian, Spinon Kondo lattice in quantum spin liquids using the slave-rotor formalism, Phys. Rev. B 110, 115116 (2024).
  15. W.-Y. He and P. A. Lee, Magnetic impurity as a local probe of the U(1) quantum spin liquid with spinon Fermi surface, Phys. Rev. B 105, 195156 (2022).
  16. S. Mishra, G. Catarina, F. Wu, R. Ortiz, D. Jacob, K. Eimre, J. Ma, C. A. Pignedoli, X. Feng, P. Ruffieux, J. Fernández-Rossier, and R. Fasel, Observation of fractional edge excitations in nanographene spin chains, Nature (London) 598, 287 (2021).
  17. C. Zhao, G. Catarina, J.-J. Zhang, J. C. G. Henriques, L. Yang, J. Ma, X. Feng, O. Gröning, P. Ruffieux, J. Fernández-Rossier, and R. Fasel, Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains, Nat. Nanotechnol. 19, 1789 (2024).
  18. C. Zhao, L. Yang, J. C. G. Henriques, M. Ferri-Cortés, G. Catarina, C. A. Pignedoli, J. Ma, X. Feng, P. Ruffieux, J. Fernández-Rossier, and R. Fasel, Spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains, Nat. Mater. 24, 722 (2025).
  19. D. Jacob, R. Ortiz, and J. Fernández-Rossier, Renormalization of spin excitations and Kondo effect in open-shell nanographenes, Phys. Rev. B 104, 075404 (2021).
  20. K. Sun, N. Cao, O. J. Silveira, A. O. Fumega, F. Hanindita, S. Ito, J. L. Lado, P. Liljeroth, A. S. Foster, and S. Kawai, On-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chains, Sci. Adv. 11, eads1641 (2025).
  21. X. Su, Z. Ding, Y. Hong, N. Ke, K. Yan, C. Li, Y.-F. Jiang, and P. Yu, Fabrication of spin-1/2 Heisenberg antiferromagnetic chains via combined on-surface synthesis and reduction for spinon detection, Nat. Synth 4, 694 (2025).
  22. E. Park, J. P. Philbin, H. Chi, J. J. Sanchez, C. Occhialini, G. Varnavides, J. B. Curtis, Z. Song, J. Klein, J. D. Thomsen, M.-G. Han, A. C. Foucher, K. Mosina, D. Kumawat, N. Gonzalez-Yepez, Y. Zhu, Z. Sofer, R. Comin, J. S. Moodera, P. Narang, et al., Anisotropic 2D van der Waals magnets hosting 1D spin chains, Adv. Mater. 36, 2401534 (2024).
  23. A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, 1998).
  24. S. Eggert and I. Affleck, Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains, Phys. Rev. B 46, 10866 (1992).
  25. Y. Wang, Exact solution of the open Heisenberg chain with two impurities, Phys. Rev. B 56, 14045 (1997).
  26. A. Furusaki and T. Hikihara, Kondo effect in XXZ spin chains, Phys. Rev. B 58, 5529 (1998).
  27. N. Laflorencie, E. S. Sørensen, and I. Affleck, The Kondo effect in spin chains, J. Stat. Mech.: Theory Exp. (2008) P02007.
  28. P. Kattel, P. R. Pasnoori, J. H. Pixley, P. Azaria, and N. Andrei, Kondo effect in the isotropic Heisenberg spin chain, Phys. Rev. B 109, 174416 (2024).
  29. A. Zhakenov, P. Kattel, and N. Andrei, Thermodynamics in a split Hilbert space: Quantum impurity at the edge of the Heisenberg chain, arXiv:2508.19334.
  30. C. P. Moca, C. Hajdú, B. Dóra, and G. Zaránd, Spectral properties of fractionalized Shiba states, Phys. Rev. Lett. 135, 126502 (2025).
  31. T. Kulka, M. Panfil, M. Berciu, and K. Wohlfeld, Nature of spinons in 1D spin chains, Phys. Rev. Lett. 134, 236504 (2025).
  32. A. Imambekov, T. L. Schmidt, and L. I. Glazman, One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm, Rev. Mod. Phys. 84, 1253 (2012).
  33. T. L. Schmidt, A. Imambekov, and L. I. Glazman, Fate of 1D spin-charge separation away from Fermi points, Phys. Rev. Lett. 104, 116403 (2010).
  34. R. G. Pereira, K. Penc, S. R. White, P. D. Sacramento, and J. M. P. Carmelo, Charge dynamics in half-filled Hubbard chains with finite on-site interaction, Phys. Rev. B 85, 165132 (2012).
  35. F. H. L. Essler, R. G. Pereira, and I. Schneider, Spin-charge-separated quasiparticles in one-dimensional quantum fluids, Phys. Rev. B 91, 245150 (2015).
  36. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  37. F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper, and V. E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press, Cambridge, 2005).
  38. P. Kattel, A. Zhakenov, and N. Andrei, Thermodynamics in a split Hilbert space: Quantum impurity at the edge of a one-dimensional superconductor, arXiv:2508.19330.
  39. F. H. L. Essler and A. M. Tsvelik, Weakly coupled one-dimensional Mott insulators, Phys. Rev. B 65, 115117 (2002).
  40. K. Penc, F. Mila, and H. Shiba, Spectral function of the 1D Hubbard model in the U→+∞ limit, Phys. Rev. Lett. 75, 894 (1995).
  41. K. A. Matveev, A. Furusaki, and L. I. Glazman, Bosonization of strongly interacting one-dimensional electrons, Phys. Rev. B 76, 155440 (2007).
  42. K.-V. Pham, M. Gabay, and P. Lederer, Fractional excitations in the Luttinger liquid, Phys. Rev. B 61, 16397 (2000).
  43. I. Affleck and A. W. W. Ludwig, The Fermi edge singularity and boundary condition changing operators, J. Phys. A: Math. Gen. 27, 5375 (1994).
  44. K. A. Hallberg, New trends in density matrix renormalization, Adv. Phys. 55, 477 (2006).
  45. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  46. T. D. Kühner and S. R. White, Dynamical correlation functions using the density matrix renormalization group, Phys. Rev. B 60, 335 (1999).
  47. K. Chen and C. Jayaprakash, Kondo effect in Fermi systems with a gap: A renormalization-group study, Phys. Rev. B 57, 5225 (1998).
  48. C. P. Moca and A. Roman, Quantum phase transition in a gapped Anderson model: A numerical renormalization group study, Phys. Rev. B 81, 235106 (2010).
  49. S.-S. Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions, Phys. Rev. B 80, 165102 (2009).
  50. M. A. Metlitski and S. Sachdev, Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order, Phys. Rev. B 82, 075127 (2010).
  51. R. G. Pereira, B. F. Marquez, K. Hallberg, T. Bauer, and R. Egger, Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators, Zenodo dataset, https://doi.org/10.5281/zenodo.17873710.
  52. I. Affleck and A. W. W. Ludwig, Critical theory of overscreened Kondo fixed points, Nucl. Phys. B 360, 641 (1991).
  53. I. Affleck, A. W. W. Ludwig, and B. A. Jones, Conformal-field-theory approach to the two-impurity Kondo problem: Comparison with numerical renormalization-group results, Phys. Rev. B 52, 9528 (1995).
  54. I. Affleck and A. W. W. Ludwig, Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green's function, self-energy, and resistivity, Phys. Rev. B 48, 7297 (1993).
  55. S. Florens and A. Georges, Quantum impurity solvers using a slave rotor representation, Phys. Rev. B 66, 165111 (2002).
  56. S. Florens and A. Georges, Slave-rotor mean-field theories of strongly correlated systems and the Mott transition in finite dimensions, Phys. Rev. B 70, 035114 (2004).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation