Skip to main content
SpringerLink
Log in

IRLM and Kondo Correlations

  • Chapter
  • First Online:
Quantum Impurity Problems in the Framework of Natural Orbitals

Part of the book series: Springer Theses ((Springer Theses))

  • 62 Accesses

Abstract

In the previous chapter, we traced the history of dilute magnetic impurities in metals and quantum dots. The SIAM and Kondo models were presented, originally introduced to describe the situation. The IRLM, a simpler variant that reports the same low energy properties that are relevant in these models, was also introduced. In this chapter, general equilibrium properties of this model are discussed without and with interactions, and problems we will focus on in the following are introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hewson AC (1993) The Kondo problem to heavy fermions. Cambridge University Press

    Google Scholar 

  2. Bruus H, Flensberg K (2004) Many-body quantum theory in condensed matter physics - an introduction (OUP Oxford, 2004)

    Google Scholar 

  3. Wilson KG (1975) The renormalization group: critical phenomena and the Kondo problem. Rev Modern Phys 47:773–840

    Article  ADS  MathSciNet  Google Scholar 

  4. Costi TA, Hewson AC, Zlatic V (1994) Transport coefficients of the Anderson model via the numerical renormalization group. J Phys: Condens Matter 6:2519–2558

    ADS  Google Scholar 

  5. Bulla R, Hewson AC, Pruschke T (1998) Numerical renormalization group calculations for the self-energy of the impurity Anderson model. J Phys: Condens Matter 10:8365–8380. ISSN: 0953-8984

    Google Scholar 

  6. Bulla R, Costi TA, Pruschke T (2008) Numerical renormalization group method for quantum impurity systems. Rev Mod Phys 80:56

    Article  Google Scholar 

  7. Oliveira WC, Oliveira LN (1994) Generalized numerical renormalization-group method to calculate the thermodynamical properties of impurities in metals. Phys Rev B 49:11986–11994. ISSN: 0163-1829, 1095-3795

    Google Scholar 

  8. Freyn A, Florens S (2009) Optimal broadening of finite energy spectra in the numerical renormalization group: application to dissipative dynamics in two-level systems. Phys Rev B 79:121102. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  9. Zitko R, Pruschke T (2009) Energy resolution and discretization artifacts in the numerical renormalization group. Phys Rev B 79:085106. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  10. Hofstetter W (2000) Generalized numerical renormalization group for dynamical quantities. Phys Rev Lett 85:4

    Article  Google Scholar 

  11. Peters R, Pruschke T, Anders FB (2006) A numerical renormalization group approach to Green’s functions for quantum impurity models. Phys Rev B 74:245114. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  12. Toth AI, Moca CP, Legeza O, Zarand G (2008) Density matrix numerical renormalization group for non-Abelian symmetries. Physical Review B 78:245109. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  13. Weichselbaum A, von Delft J (2007) Sum-rule conserving spectral functions from the numerical renormalization group. Phys Rev Lett 99:076402. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  14. Ishii H, Yosida K (1967) Zero-temperature susceptibility of a localized spin exchange coupled with the conduction electrons. Progress Theor Phys 38:61–71. ISSN: 0033-068X

    Google Scholar 

  15. Müller-Hartmann, E. Spin correlation in dilute magnetic alloys. en. Zeitschrift für Physik A Hadrons and nuclei 223, 277-288. issn: 0939-7922 (1969)

    Google Scholar 

  16. Ishii H (1978) Spin correlation in dilute magnetic alloys. J Low Temp Phys 32:11

    Article  Google Scholar 

  17. Chen K, Jayaprakash C, Krishna-Murthy HR (1987) Spatial correlations around a Kondo impurity. Phys Rev Lett 58:929–932

    Article  ADS  Google Scholar 

  18. Chen K, Jayaprakash C, Krishnamurthy HR (1992) Spatially dependent zero-frequency response functions and correlation functions in the Kondo model. Phys Rev B 45:5368–5386

    Article  ADS  Google Scholar 

  19. Sorensen ES, Affleck I (1996) Scaling theory of the Kondo screening cloud. Phys Rev B 53:9153–9167

    Article  ADS  Google Scholar 

  20. Barzykin V, Affleck I (1996) The Kondo Screening Cloud: What Can We Learn from Perturbation Theory? Phys Rev Lett 76:4959–4962

    Article  ADS  Google Scholar 

  21. Barzykin V, Affleck I (1998) Screening cloud in the k-channel Kondo model: perturbative and large-k results. Phys Rev B 57:432–448

    Article  ADS  Google Scholar 

  22. Cornaglia PS, Balseiro CA (2002) Kondo impurities in nanoscopic systems: confinementinduced regimes. Phys Rev B 66:115303

    Article  ADS  Google Scholar 

  23. Costamagna S, Gazza CJ, Torio ME, Riera JA (2006) Anderson impurity in the one-dimensional Hubbard model for finite-size systems. Phys Rev B 74:195103

    Article  ADS  Google Scholar 

  24. Molina RA, Weinmann D, Pichard J-L (2006) Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds, 0507571. arXiv:condmat/

  25. Hand T, Kroha J, Monien H (2006) Spin correlations and finite-size effects in the one-dimensional Kondo Box. arXiv:cond-mat/0602352

  26. Borda L (2007) Kondo screening cloud in a one-dimensional wire: numerical renormalization group study. Phys Rev B 75:041307. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  27. Sørensen ES, Chang M-S, Laflorencie N, Affleck I (2007) Impurity entanglement entropy and the Kondo screening cloud. J Stat Mech: Theory Exper 2007:L01001–L01001. ISSN: 1742-5468

    Google Scholar 

  28. Affleck I, Borda L, Saleur H (2008) Friedel oscillations and the Kondo screening cloud. Phys Rev B 77:180404. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  29. Holzner A, McCulloch IP, Schollwöck U, von Delft J, Heidrich-Meisner F (2009) Kondo screening cloud in the single-impurity Anderson model: a density matrix renormalization group study. Phys Rev B 80:205114

    Article  ADS  Google Scholar 

  30. Büsser CA et al (2010) Numerical analysis of the spatial range of the Kondo effect. Phys Rev B 81:045111

    Article  ADS  Google Scholar 

  31. Mitchell AK, Becker M, Bulla R (2011) Real-space renormalization group flow in quantum impurity systems: Local moment formation and the Kondo screening cloud. Phys Rev B 84:115120

    Article  ADS  Google Scholar 

  32. Feng X-Y, Zhang F-C (2011) Kondo spin screening cloud in two-dimensional electron gas with spin-orbit couplings. J Phy: Condens Matter 23:105602. ISSN: 0953-8984, 1361-648X

    Google Scholar 

  33. Posske T, Liu C-X, Budich JC, Trauzettel B (2013) Exact results for the Kondo screening cloud of two helical liquids. Phys Rev Lett 110:016602. ISSN: 1079-7114

    Google Scholar 

  34. Medvedyeva M, Hoffmann A, Kehrein S (2013) Spatiotemporal buildup of the Kondo screening cloud. Phys Rev B 88:094306

    Article  ADS  Google Scholar 

  35. Ghosh S, Ribeiro P, Haque M (2014) Real-space structure of the impurity screening cloud in the resonant level model. J Stat Mech: Theory Exper 2014:P04011. ISSN: 1742-5468

    Google Scholar 

  36. Florens S, Snyman I (2015) Universal spatial correlations in the anisotropic Kondo screening cloud: analytical insights and numerically exact results from a coherent state expansion. Phys Rev B 92:195106

    Article  ADS  Google Scholar 

  37. Lee S, Park J, Sim H (2015) Macroscopic quantum entanglement of a Kondo cloud at finite temperature. Phys Rev Lett 114:057203. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  38. Nuss M, Ganahl M, Arrigoni E, von der Linden W, Evertz HG (2015) Nonequilibrium spatiotemporal formation of the Kondo screening cloud on a lattice. Phys Rev B 91:085127

    Article  ADS  Google Scholar 

  39. Ribeiro LC, Martins GB, Gómez-Silva G, Anda EV (2019) Numerical study of the Kondo cloud using finite-U slave bosons. Phys Rev B 99:085139. ISSN: 2469-9950, 2469-9969

    Google Scholar 

  40. Diniz G, Diniz GS, Martins GB, Vernek E (2020) Reentrant Kondo effect for a quantum impurity coupled to a metal-semiconductor hybrid contact. Phys Rev B 101:125115. ISSN: 2469-9950, 2469-9969

    Google Scholar 

  41. Moca CP, Weymann I, Werner MA, Zaránd G (2021) Kondo cloud in a superconductor. Phys Rev Lett 127:186804. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  42. Mukherjee A, Mukherjee A, Vidhyadhiraja NS, Taraphder A, Lal S (2022) Unveiling the Kondo cloud: unitary renormalization-group study of the Kondo model. Phys Rev B 105:085119. ISSN: 2469-9950, 2469-9969

    Google Scholar 

  43. Barzykin V, Affleck I (1998) Screening cloud in the \(k\)-channel Kondo model: perturbative and large-\(k\) results. Phys Rev B 57:432–448

    Article  ADS  Google Scholar 

  44. Borzenets, I. V. et al. Observation of the Kondo screening cloud. en. Nature, 11 (2020)

    Google Scholar 

  45. Affleck I, Simon P (2001) Detecting the Kondo screening cloud around a quantum dot. Phys Rev Lett 86:2854–2857

    Article  ADS  Google Scholar 

  46. Cornaglia PS, Balseiro CA (2003) Transport through Quantum dots in mesoscopic circuits. Phys Rev Lett 90:216801

    Google Scholar 

  47. Pereira RG, Laflorencie N, Affleck I, Halperin BI (2008 ) Kondo screening cloud and charge staircase in one-dimensional mesoscopic devices. Phys Rev B 77:125327

    Google Scholar 

  48. Patton KR, Hafermann H, Brener S, Lichtenstein AI, Katsnelson MI (2009) Probing the Kondo screening cloud via tunneling-current conductance fluctuations. Phys Rev B 80:212403

    Google Scholar 

  49. Nishida Y (2013) SU(3) orbital Kondo effect with ultracold atoms. Phys Rev Lett 111:135301

    Google Scholar 

  50. Bauer J, Salomon C, Demler E (2013) Realizing a Kondo-correlated state with ultracold atoms. Phys Rev Lett 111:215304

    Google Scholar 

  51. Snyman I, Florens S (2015) Robust Josephson-Kondo screening cloud in circuit quantum electrodynamics. Phys Rev B 92:085131

    Google Scholar 

  52. Affleck I (2009) The Kondo screening cloud: what it is and how to observe it. arXiv

    Google Scholar 

  53. Park J, Lee S, Oreg Y, Sim H (2013) How to directly measure a kondo cloud’s length. Phys Rev Lett 110:246603. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  54. Moca CP, Weymann I, Werner MA, Zaránd G (2021) Kondo cloud in a superconductor. Phys Rev Lett 127:186804

    Google Scholar 

  55. Erpenbeck A, Cohen G (2021) Resolving the nonequilibrium Kondo singlet in energyand position-space using quantum measurements. SciPost Phys 10

    Google Scholar 

  56. Figgins J et al (2019) Quantum engineered Kondo lattices. Nat Commun 10:5588. ISSN: 2041-1723

    Google Scholar 

  57. Prüser H et al (2011) Long-range Kondo signature of a single magnetic impurity. Nat Phys 7:203–206. ISSN: 1745-2473, 1745-2481

    Google Scholar 

  58. Jiang Y, Zhang YN, Cao JX, Wu RQ, Ho W (2011) Real-space imaging of Kondo screening in a two-Dimensional O2 lattice. Science 333:324–328

    Article  ADS  Google Scholar 

  59. Seaman CL et al (1991) Evidence for non-Fermi-liquid behavior in the Kondo alloy Y1-xUxPdd. Phys Rev Lett 67:2882–2885

    Article  ADS  Google Scholar 

  60. MacLaughlin DE et al (2004) Disorder, inhomogeneity and spin dynamics in f-electron non-Fermi liquid systems. J Phys: Condens Matter 16:S4479–S4498

    Google Scholar 

  61. Aronson MC et al (1995) Non-Fermi-liquid scaling of the magnetic response in UCu5-xPdx(x = 1, 1.5). Phys Rev Lett 75:725–728

    Google Scholar 

  62. Bernal OO, MacLaughlin DE, Lukefahr HG, Andraka B (1995) Copper NMR and thermodynamics of UCu5-xPdx: evidence for Kondo disorder. Phys Rev Lett 75:2023–2026

    Google Scholar 

  63. Löhneysen Hv et al (1994) Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability. Phys Rev Lett 72:3262–3265

    Google Scholar 

  64. Maple MB et al (1994) Non-Fermi liquid ground states in strongly correlated f-electron materials. J Appl Phys 76:6137–6137

    Article  ADS  Google Scholar 

  65. Dobrosavljević V, Kirkpatrick TR, Kotliar BG (1992) Kondo effect in disordered systems. Phys Rev Lett 69:1113–1116

    Article  ADS  Google Scholar 

  66. Miranda E, Dobrosavljevic V, Kotliar G (1997) Disorder-driven non-Fermi liquid behavior in Kondo alloys. Phys Rev Lett 78:290–293. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  67. Cornaglia PS, Grempel DR, Balseiro CA (2006) Universal Distribution of Kondo Temperatures in Dirty Metals. Phys Rev Lett 96:117209

    Article  ADS  Google Scholar 

  68. Kettemann, S. & Mucciolo, E. R. Free magnetic moments in disordered metals. en. Journal of Experimental and Theoretical Physics Letters 83, 240-245. issn: 0021- 3640, 1090-6487 (2006)

    Google Scholar 

  69. Kaul RK, Ullmo D, Baranger HU (2003) Mesoscopic fluctuations in quantum dots in the Kondo regime. Phys Rev B 68:161305. ISSN: 0163-1829, 1095-3795

    Google Scholar 

  70. Nagaoka Y (1965) Self-consistent treatment of Kondo’s effect in dilute alloys. Phys Rev 138:A1112–A1120

    Article  ADS  Google Scholar 

  71. Milovanović M, Sachdev S, Bhatt RN (1989) Effective-field theory of local-moment formation in disordered metals. Phys Rev Lett 63:82–85. ISSN: 0031- 9007

    Google Scholar 

  72. Martin I, Wan Y, Phillips P (1997) Size dependence in the disordered Kondo problem. Phys Rev Lett 78:114–117. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  73. Miranda E, Dobrosavljević V (2001) Localization-induced Griffiths phase of disordered Anderson lattices. Phys Rev Lett 86:264–267. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  74. Cornaglia PS, Balseiro CA (2002) Kondo impurities in nanoscopic systems: confinementinduced regimes. Phys Rev B 66:115303

    Article  ADS  Google Scholar 

  75. Micklitz T, Altland A, Costi TA, Rosch A (2006) Universal dephasing rate due to diluted Kondo impurities. Phys Rev Lett 96:226601. ISSN: 0031-9007, 1079-7114

    Google Scholar 

  76. Kettemann S, Mucciolo ER, Varga I, Slevin K (2012) Kondo-Anderson transitions. Phys Rev B 85:115112. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  77. Kettemann S, Mucciolo ER (2007) Disorder-quenched Kondo effect in mesoscopic electronic systems. Phys Rev B 75:184407. ISSN: 1098-0121, 1550-235X

    Google Scholar 

  78. Zhuravlev A et al (2007) Nonperturbative scaling theory of free magnetic moment phases in disordered metals. Phys Rev Lett 99:247202. ISSN: 0031- 9007, 1079-7114

    Google Scholar 

  79. Bergmann G, Thompson RS (2014) The range of the Kondo cloud in weakly disordered hosts. arXiv:1410.7512 [cond-mat]

  80. Miranda VG (2014) Dias da Silva LGGV, Lewenkopf CH (2014) Disorder-mediated Kondo effect in graphene. Phys Rev B 90:201101. ISSN: 1098-0121, 1550- 235X

    Google Scholar 

  81. Moure N, Lee H-Y, Haas S, Bhatt RN, Kettemann S (2018) Disordered quantum spin chains with long-range antiferromagnetic interactions. Phys Rev B 97:014206. ISSN: 2469-9950, 2469-9969

    Google Scholar 

  82. Park K-Y, Jang I, Kim K-S, Kettemann S (2021) Inhomogeneous Kondo destruction by RKKY correlations. Ann Phys 435:168501. ISSN: 00034916

    Google Scholar 

  83. Sen S, Vidhyadhiraja NS, Jarrell M (2018) Emergence of non-Fermi liquid dynamics through nonlocal correlations in an interacting disordered system. Phys Rev B 98:075112

    Article  ADS  Google Scholar 

  84. Slevin K, Kettemann S, Ohtsuki T (2019) Multifractality and the distribution of the Kondo temperature at the Anderson transition. Eur Phys J B 92:281. ISSN: 1434-6028, 1434-6036

    Google Scholar 

  85. Beenakker CWJ (1997) Random-matrix theory of quantum transport. Rev Mod Phys 69:731–808

    Article  ADS  Google Scholar 

  86. Liu DE, Burdin S, Baranger HU, Ullmo D (2012) Mesoscopic Anderson box: connecting weak to strong coupling. Phys Rev B 85:155455

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Institute, University of Bonn, Bonn, Germany

    Maxime Debertolis

Authors
  1. Maxime Debertolis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maxime Debertolis .

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Debertolis, M. (2024). IRLM and Kondo Correlations. In: Quantum Impurity Problems in the Framework of Natural Orbitals. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-031-47233-6_2

Download citation

Publish with us

Policies and ethics

Search

Navigation