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Relevance of anisotropy in the Kondo effect: Lessons from the symplectic case

Matan Lotem1,2,*, Sarath Sankar1, Tianhao Ren3, Moshe Goldstein1, Elio. J. König4, Andreas Weichselbaum3, Eran Sela1, and Alexei M. Tsvelik3,†

  • *Contact author: matanlotem@post.bgu.ac.il
  • †Contact author: atsvelik@bnl.gov
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Phys. Rev. B 110, 235122 – Published 9 December, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.235122

Abstract

A Kondo model with symplectic symmetry was recently put forward as the effective low-energy theory of a superconducting-island device coupled to multiple leads. This model, which possesses non-Fermi liquid physics and effective anyons, was argued to belong to the class of topological Kondo effects. Here, we clarify the extent of stability of its exotic fixed point using perturbative and numerical renormalization group in conjunction with bosonization and conformal field theory. In contrast to previous claims, we show that asymmetry in the coupling to the leads destabilizes the non-Fermi liquid. Other destabilizing perturbations include asymmetry in the superconducting pairing or internal energy of the individual quantum dots in the island. Nevertheless, these perturbations all generate the same relevant operators. Thus, only a small number of couplings need to be tuned individually, and these can be selected according to experimental convenience. Our results highlight a common misconception that anisotropy in single-channel Kondo couplings is always irrelevant. As demonstrated, relevant terms will emerge whenever the group generators do not span the full space of impurity operators. This calls for a more detailed inspection of models that exhibit this property, such as large-spin impurities and SO(M) Kondo models.

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References (65)

  1. A. M. Tsvelick, The thermodynamics of multichannel Kondo problem, J. Phys. C: Solid State Phys. 18, 159 (1985).
  2. 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).
  3. R. M. Potok, I. G. Rau, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Observation of the two-channel Kondo effect, Nature (London) 446, 167 (2007).
  4. A. J. Keller, L. Peeters, C. P. Moca, I. Weymann, D. Mahalu, V. Umansky, G. Zaránd, and D. Goldhaber-Gordon, Universal Fermi liquid crossover and quantum criticality in a mesoscopic system, Nature (London) 526, 237 (2015).
  5. Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. D. Parmentier, A. Cavanna, and F. Pierre, Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states, Nature (London) 526, 233 (2015).
  6. Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, and F. Pierre, Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit, Science 360, 1315 (2018).
  7. W. Pouse, L. Peeters, C. L. Hsueh, U. Gennser, A. Cavanna, M. A. Kastner, A. K. Mitchell, and D. Goldhaber-Gordon, Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit, Nat. Phys. 19, 492 (2023).
  8. P. L. S. Lopes, I. Affleck, and E. Sela, Anyons in multichannel Kondo systems, Phys. Rev. B 101, 085141 (2020).
  9. D. Gabay, C. Han, P. L. S. Lopes, I. Affleck, and E. Sela, Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules, Phys. Rev. B 105, 035151 (2022).
  10. M. Lotem, E. Sela, and M. Goldstein, Chiral numerical renormalization group, Phys. Rev. B 107, 155417 (2023).
  11. M. Lotem, E. Sela, and M. Goldstein, Manipulating Non-Abelian anyons in a chiral multichannel Kondo model, Phys. Rev. Lett. 129, 227703 (2022).
  12. Y. Komijani, Isolating Kondo anyons for topological quantum computation, Phys. Rev. B 101, 235131 (2020).
  13. T. Ren, E. J. König, and A. M. Tsvelik, Topological quantum computation on a chiral Kondo chain, Phys. Rev. B 109, 075145 (2024).
  14. D. L. Cox and A. Zawadowski, Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres, Adv. Phys. 47, 599 (1998).
  15. R. M. Konik, H. Saleur, and A. W. W. Ludwig, Interplay of the scaling limit and the renormalization group: Implications for symmetry restoration, Phys. Rev. B 66, 075105 (2002).
  16. P. D. Kurilovich, V. D. Kurilovich, I. S. Burmistrov, and M. Goldstein, Helical edge transport in the presence of a magnetic impurity, JETP Lett. 106, 575 (2017).
  17. E. Kogan, Poor man's scaling: anisotropic Kondo and Coqblin– Schrieffer models, J. Phys. Commun. 2, 085001 (2018).
  18. E. Kogan, Poor man's scaling and Lie algebras, J. Phys. Commun. 3, 125001 (2019).
  19. E. Kogan and Z. Shi, Poor man's scaling: XYZ Coqblin–Schrieffer model revisited, J. Stat. Mech. (2021) 033101.
  20. B. Béri and N. R. Cooper, Topological Kondo effect with Majorana fermions, Phys. Rev. Lett. 109, 156803 (2012).
  21. A. Altland and R. Egger, Multiterminal Coulomb-Majorana junction, Phys. Rev. Lett. 110, 196401 (2013).
  22. B. Béri, Majorana-Klein hybridization in topological superconductor junctions, Phys. Rev. Lett. 110, 216803 (2013).
  23. A. Altland, B. Béri, R. Egger, and A. M. Tsvelik, Multichannel Kondo impurity dynamics in a Majorana device, Phys. Rev. Lett. 113, 076401 (2014).
  24. A. Altland, B. Béri, R. Egger, and A. M. Tsvelik, Bethe Ansatz solution of the topological Kondo model, J. Phys. A: Math. Theor. 47, 265001 (2014).
  25. M. R. Galpin, A. K. Mitchell, J. Temaismithi, D. E. Logan, B. Béri, and N. R. Cooper, Conductance fingerprint of Majorana fermions in the topological Kondo effect, Phys. Rev. B 89, 045143 (2014).
  26. F. Buccheri, H. Babujian, V. E. Korepin, P. Sodano, and A. Trombettoni, Thermodynamics of the topological Kondo model, Nucl. Phys. B 896, 52 (2015).
  27. L. Herviou, K. Le Hur, and C. Mora, Many-terminal Majorana island: From topological to multichannel Kondo model, Phys. Rev. B 94, 235102 (2016).
  28. B. Béri, Exact nonequilibrium transport in the topological Kondo effect, Phys. Rev. Lett. 119, 027701 (2017).
  29. K. Michaeli, L. A. Landau, E. Sela, and L. Fu, Electron teleportation and statistical transmutation in multiterminal Majorana islands, Phys. Rev. B 96, 205403 (2017).
  30. L. A. Landau and E. Sela, Two-channel Kondo physics in a Majorana island coupled to a Josephson junction, Phys. Rev. B 95, 035135 (2017).
  31. K. Snizhko, F. Buccheri, R. Egger, and Y. Gefen, Parafermionic generalization of the topological Kondo effect, Phys. Rev. B 97, 235139 (2018).
  32. A. K. Mitchell, A. Liberman, E. Sela, and I. Affleck, SO(5) Non-Fermi liquid in a Coulomb box device, Phys. Rev. Lett. 126, 147702 (2021).
  33. A. Liberman, A. K. Mitchell, I. Affleck, and E. Sela, SO(5) critical point in a spin-flavor Kondo device: Bosonization and refermionization solution, Phys. Rev. B 103, 195131 (2021).
  34. G. Li, Y. Oreg, and J. I. Väyrynen, Multichannel topological Kondo effect, Phys. Rev. Lett. 130, 066302 (2023).
  35. M. M. Wauters, C.-M. Chung, L. Maffi, and M. Burrello, Topological Kondo model out of equilibrium, Phys. Rev. B 108, L220302 (2023).
  36. S. Bollmann, J. I. Väyrynen, and E. J. König, Topological Kondo effect with spinful Majorana fermions, Phys. Rev. B 110, 035136 (2024).
  37. T. Kimura, ABCD of Kondo effect, J. Phys. Soc. Jpn. 90, 024708 (2021).
  38. G. Li, E. J. König, and J. I. Väyrynen, Topological symplectic Kondo effect, Phys. Rev. B 107, L201401 (2023).
  39. E. J. König and A. M. Tsvelik, Exact solution of the topological symplectic Kondo problem, Ann. Phys. (NY) 456, 169231 (2023).
  40. K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
  41. R. Bulla, T. A. Costi, and T. Pruschke, Numerical renormalization group method for quantum impurity systems, Rev. Mod. Phys. 80, 395 (2008).
  42. V. J. Emery and S. Kivelson, Mapping of the two-channel Kondo problem to a resonant-level model, Phys. Rev. B 46, 10812 (1992).
  43. R. Flint, M. Dzero, and P. Coleman, Heavy electrons and the symplectic symmetry of spin, Nat. Phys. 4, 643 (2008).
  44. R. Flint and P. Coleman, Symplectic N and time reversal in frustrated magnetism, Phys. Rev. B 79, 014424 (2009).
  45. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  46. H. Georgi, Lie Algebras In Particle Physics: From Isospin To Unified Theories (CRC Press, Boca Raton, Fl, 2019)
  47. P. W. Anderson, A poor man's derivation of scaling laws for the Kondo problem, J. Phys. C: Solid State Phys. 3, 2436 (1970).
  48. R. Žitko, R. Peters, and Th. Pruschke, Properties of anisotropic magnetic impurities on surfaces, Phys. Rev. B 78, 224404 (2008).
  49. M. A. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev. 96, 99 (1954).
  50. T. Kasuya, A Theory of metallic ferro- and antiferromagnetism on Zener's model, Prog. Theor. Phys. 16, 45 (1956).
  51. K. Yosida, Magnetic properties of Cu-Mn alloys, Phys. Rev. 106, 893 (1957).
  52. A. Schiller and L. De Leo, Phase diagram of the anisotropic multichannel Kondo Hamiltonian revisited, Phys. Rev. B 77, 075114 (2008).
  53. G. Zaránd and J. von Delft, Analytical calculation of the finite-size crossover spectrum of the anisotropic two-channel Kondo model, Phys. Rev. B 61, 6918 (2000).
  54. J. von Delft, G. Zaránd, and M. Fabrizio, Finite-size bosonization of 2-channel Kondo model: A bridge between numerical renormalization group and conformal field theory, Phys. Rev. Lett. 81, 196 (1998).
  55. E. Sela and I. Affleck, Nonequilibrium critical behavior for electron tunneling through quantum dots in an Aharonov-Bohm circuit, Phys. Rev. B 79, 125110 (2009).
  56. E. Sela and I. Affleck, Nonequilibrium transport through double quantum dots: Exact results near a quantum critical point, Phys. Rev. Lett. 102, 047201 (2009).
  57. P. Bouwknegt and K. Schoutens, Exclusion statistics in conformal field theory—Generalized fermions and spinons for level-1 WZW theories, Nucl. Phys. B 547, 501 (1999).
  58. I. Affleck, Conformal field theory approach to the Kondo effect, arXiv:cond-mat/9512099.
  59. A. Weichselbaum, Non-Abelian symmetries in tensor networks: A quantum symmetry space approach, Ann. Phys. (NY) 327, 2972 (2012).
  60. A. Weichselbaum, QSpace – An open-source tensor library for Abelian and non-Abelian symmetries, SciPost Phys. Codebases 40 (2024).
  61. P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, 2015).
  62. A. Weichselbaum, X-symbols for non-Abelian symmetries in tensor networks, Phys. Rev. Res. 2, 023385 (2020).
  63. S.-S. B. Lee and A. Weichselbaum, Adaptive broadening to improve spectral resolution in the numerical renormalization group, Phys. Rev. B 94, 235127 (2016).
  64. A. K. Mitchell, M. R. Galpin, S. Wilson-Fletcher, D. E. Logan, and R. Bulla, Generalized Wilson chain for solving multichannel quantum impurity problems, Phys. Rev. B 89, 121105(R) (2014).
  65. K. M. Stadler, A. K. Mitchell, J. von Delft, and A. Weichselbaum, Interleaved numerical renormalization group as an efficient multiband impurity solver, Phys. Rev. B 93, 235101 (2016).

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Phys. Rev. B 110, 235122– Published 9 December, 2024
  • Received 6 August 2024
  • Accepted 28 October 2024
Article part of CHORUS
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