Quick Search:
Author: Title/Abstract: Vol./No: Page:

Prog. Theor. Phys. Vol. 53 No. 5 (1975) pp. 1286-1301

[ Full Text PDF : FREE ACCESS (911K) ]

Perturbation Expansion for the Anderson Hamiltonian. III

Kei Yosida and Kosaku Yamada

Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo

(Received November 8, 1974)

Abstract:

Thermodynamical quantities are expanded in perturbation series with respect to the Coulomb repulsion U for the Anderson Hamiltonian with electron-hole symmetry and their general terms of perturbation are investigated. By these processes the mutual relations among these quantities are discussed. it is confirmed that the thermodynamical quantities such as the specific heat and the scattering t-matrix are expressed in terms of two quantities; the even and odd parts of the susceptibility as far as low-lying excitations are concerned. These results are entirely consistent with the Nozières phenomenological Fermi liquid theory based on the s-d exchange model.


URL : http://ptp.ipap.jp/link?PTP/53/1286/
DOI : 10.1143/PTP.53.1286

[ Full Text PDF : FREE ACCESS (911K) ] Citation:


References:

  1. K. Yosida and K. Yamada, Prog. Theor. Phys. Suppl. No. 46 (1970), 244[PTP].
  2. P. W. Anderson, Phys. Rev. 124 (1961), 41[APS].
  3. K. Yamada, Prog. Theor. Phys. 53 (1975), 970[PTP].
  4. N. Menyhárd, Solid State Commun. 12 (1973), 215[CrossRef].
  5. P. Nozières, J. Low Temp. Phys. 17 (1974), 31[CrossRef].
  6. W. Brenig and J. Zittartz, Magnetism, edited by H. Suhl (Academic Press, 1973), Vol. V, p. 185.
  7. P. W. Anderson and G. Yuval, Magnetism, edited by H. Suhl (Academic Press, 1973), Vol. V, p. 217.
  8. K. Yosida and A. Yoshimori, Magnetism, edited by H. Suhl (Academic Press, 1973), Vol. V, p. 253.
  9. K. Wilson, Collective Properties of Physical Systems, Nobel Symposium 24 (Academic Press, 1974).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 2098-2103 :
    Kondo Effect and Mutual Interaction in One-Dimension
    Tadao Sugiyama
  2. Journal of the Physical Society of Japan 56 (1987) pp. 3667-3676 :
    Crystal-Field Effects on Low-Frequency Susceptibility for Ce-Kondo System
    Atsunobu Nakamura, Norio Kawakami and Ayao Okiji
  3. Journal of the Physical Society of Japan 57 (1988) pp. 1687-1698 :
    Critical Study of the Anderson Impurity and the Anderson Lattice
    Biao Jin and Yoshihiro Kuroda
  4. Journal of the Physical Society of Japan 57 (1988) pp. 3920-3931 :
    Theory of Superconductivity in Strongly Correlated Systems: Auxiliary Boson-Fermion Formulation
    Fusayoshi J. Ohkawa
  5. Journal of the Physical Society of Japan 57 (1988) pp. 4359-4365 :
    Crystal-Field Effects on Thermoelectric Power and Resistivity for the Ce-Kondo System
    Norio Kawakami, Atsunobu Nakamura and Ayao Okiji
  6. Journal of the Physical Society of Japan 58 (1989) pp. 3666-3678 :
    Single-Particle and Magnetic Excitation Spectra of Degenerate Anderson Model with Finite ff Coulomb Interaction
    Osamu Sakai, Yukihiro Shimizu and Tadao Kasuya
  7. Journal of the Physical Society of Japan 58 (1989) pp. 4156-4167 :
    Auxiliary-Particle Theory of Strongly Correlated Systems
    Fusayoshi J. Ohkawa
  8. Journal of the Physical Society of Japan 58 (1989) pp. 4557-4568 :
    Proximity Induced Meissner Effect in Dirty Normal Metals
    Osamu Narikiyo and Hidetoshi Fukuyama
  9. Journal of the Physical Society of Japan 59 (1990) pp. 2831-2840 :
    Quantum Phenomenology for Heavy-Fermion Systems. I. Formulation of the Duality Model
    Yoshio Kuramoto and Kazumasa Miyake
  10. Journal of the Physical Society of Japan 60 (1991) pp. 3218-3221 :
    Electron Correlation in the Hubbard Modelin d=∞ Dimension
    Fusayoshi J. Ohkawa
  11. Journal of the Physical Society of Japan 61 (1992) pp. 631-638 :
    Meissner Effect Due to Cooper Pairs between Bloch Electrons: Analysis of Penetration Depth of YBa 2Cu 3O 7
    Fusayoshi J. Ohkawa
  12. Journal of the Physical Society of Japan 61 (1992) pp. 639-648 :
    Second Superconducting Transition Driven by Charge Density Wave
    Fusayoshi J. Ohkawa
  13. Journal of the Physical Society of Japan 61 (1992) pp. 952-959 :
    Optical Conductivity of Heavy-Electron Liquids in the Mott-Transition Region
    Fusayoshi J. Ohkawa
  14. Journal of the Physical Society of Japan 61 (1992) pp. 1157-1160 :
    Coherence Peaks of NMR and Dynamic Conductivity in Anisotropic Superconductors
    Fusayoshi J. Ohkawa
  15. Journal of the Physical Society of Japan 61 (1992) pp. 1615-1632 :
    Electron Correlation in the Hubbard Model in d=+∞ Dimension: Heavy Electrons in the Mott-Transition Region
    Fusayoshi J. Ohkawa
  16. Journal of the Physical Society of Japan 61 (1992) pp. 3239-3254 :
    Numerical Renormalization Group Study of Magnetic Impurities in Superconductors
    Koji Satori, Hiroyuki Shiba, Osamu Sakai and Yukihiro Shimizu
  17. Journal of the Physical Society of Japan 61 (1992) pp. 4490-4501 :
    Local Kondo Temperature of Strongly Correlated Electron Liquids
    Fusayoshi J. Ohkawa
  18. Journal of the Physical Society of Japan 61 (1992) pp. 4521-4535 :
    Superconductivity in the Hubbard Model
    Fusayoshi J. Ohkawa
  19. Journal of the Physical Society of Japan 63 (1994) pp. 602-614 :
    On the Superexchange Interaction in the Hubbard Model
    Fusayoshi J. Ohkawa and Naoyuki Matsumoto
  20. Journal of the Physical Society of Japan 65 (1996) pp. 1769-1781 :
    A Theory of Anisotropic Semiconductor of Heavy Fermions
    Hiroaki Ikeda and Kazumasa Miyake
  21. Journal of the Physical Society of Japan 66 (1997) pp. 1427-1437 :
    Fermi-Liquid Theory for a Conductance through an Interacting Region Attached to Noninteracting Leads
    Akira Oguri
  22. Journal of the Physical Society of Japan 66 (1997) pp. 1512-1525 :
    Excitation Spectra of the Anderson Model with Charge Screening through d- f Coulomb Interaction
    Ryu Takayama and Osamu Sakai
  23. Journal of the Physical Society of Japan 66 (1997) pp. 2389-2398 :
    Renormalized Perturbation Approach for Examination of Itinerant-Localized Duality Model for Strongly Correlated Electron Systems
    Yukihiro Okuno, Osamu Narikiyo and Kazumasa Miyake
  24. Journal of the Physical Society of Japan 68 (1999) pp. 309-310 :
    Resistivity due to Kondo Impurities near Magnetic Quantum Critical Point
    Osamu Narikiyo and Kazumasa Miyake
  25. Journal of the Physical Society of Japan 70 (2001) pp. 2666-2681 :
    Transmission Probability for Interacting Electrons Connected to Reservoirs
    Akira Oguri
  26. Journal of the Physical Society of Japan 71 (2002) pp. 1126-1133 :
    Possible Mechanism of Superconductivity in Ce-Based Heavy Fermion Compounds: Analysis Based on the Third-Order Perturbation Theory
    Hiroaki Ikeda
  27. Journal of the Physical Society of Japan 73 (2004) pp. 163-172 :
    Effects of Electron Correlation on the Transport through a Quantum Dot Superlattice
    Yoshihide Tanaka and Akira Oguri
  28. Journal of the Physical Society of Japan 73 (2004) pp. 515-518 :
    Generalized Kadowaki–Woods Relation in Heavy Fermion Systems with Orbital Degeneracy
    Hiroshi Kontani
  29. Journal of the Physical Society of Japan 74 (2005) pp. 8-15 :
    The Strong Coupling Fixed-Point Revisited
    A. C. Hewson
  30. Journal of the Physical Society of Japan 74 (2005) pp. 27-33 :
    Kondo Effect in Systems with Two-Electron Occupancy
    Yukihiro Shimizu and Osamu Sakai
  31. Journal of the Physical Society of Japan 74 (2005) pp. 67-72 :
    Kondo Problem and Related One-dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory
    Satoshi Fujimoto and Norio Kawakami
  32. Journal of the Physical Society of Japan 74 (2005) pp. 110-117 :
    Fermi Liquid Theory for the Nonequilibrium Kondo Effect at Low Bias Voltages
    Akira Oguri
  33. Journal of the Physical Society of Japan 74 (2005) pp. 127-135 :
    Out-of-Equilibrium Transport Phenomena through a Quantum Dot in a Magnetic Field
    Tatsuya Fujii and Kazuo Ueda
  34. Journal of the Physical Society of Japan 74 (2005) pp. 988-996 :
    NRG Approach to the Transport through a Finite Hubbard Chain Connected to Reservoirs
    Akira Oguri and A. C. Hewson
  35. Journal of the Physical Society of Japan 74 (2005) pp. 3340-3350 :
    Crossover between Local-Moment Magnetism and Itinerant-Electron Magnetism in the tJ Model
    Fusayoshi J. Ohkawa
  36. Journal of the Physical Society of Japan 76 (2007) 084702 (8 pages) :
    Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon
    Takashi Hotta
  37. Journal of the Physical Society of Japan 76 (2007) 104704 (14 pages) :
    Perturbative Approach to Coulomb Interaction in Double Quantum Dot Systems
    Satoshi Kawaguchi
  38. Journal of the Physical Society of Japan 77 (2008) 064707 (16 pages) :
    Fourth-Order Perturbation Expansion for Hubbard Model on a Two-Dimensional Square Lattice
    Hiroaki Ikeda, Shogo Shinkai, and Kosaku Yamada
  39. Journal of the Physical Society of Japan 80 (2011) 064701 (14 pages) :
    Kondo Effect of a Magnetic Ion Vibrating in a Harmonic Potential
    Satoshi Yashiki, Shunsuke Kirino, Kazumasa Hattori, and Kazuo Ueda
  40. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 316-324 :
    Perturbation Expansion for the Anderson Hamiltonian. IV
    Kosaku Yamada
  41. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 967-981 :
    The Korringa Relation for the Impurity Nuclear Spin-Lattice Relaxation in Dilute Kondo Alloys
    Hiroyuki Shiba
  42. Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 67-80 :
    Perturbation Analysis on Orbital-Degenerate Anderson Model
    Akio Yoshimori
  43. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1345-1355 :
    Thermodynamical Quantities in the Anderson Hamiltonian
    Kosaku Yamada
  44. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1373-1383 :
    Spin Polarization in the Anderson Model
    Hiroumi Ishii
  45. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 713-733 :
    Theory of Kondo Effect in Superconductors. I
    Tamifusa Matsuura, Shin'ichi Ichinose and Yosuke Nagaoka
  46. Progress of Theoretical Physics Vol. 57 No. 6 (1977) pp. 1823-1835 :
    The Effects of Impurities on Superconductors with Kondo Effect
    Tamifusa Matsuura
  47. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 404-418 :
    Theory of Kondo Effect in Superconductors. II
    Shin'ichi Ichinose
  48. Progress of Theoretical Physics Vol. 59 No. 1 (1978) pp. 34-39 :
    Orthogonality Catastrophe due to Local Electron Correlation
    Hiroyuki Kaga and Kei Yosida
  49. Progress of Theoretical Physics Vol. 62 No. 2 (1979) pp. 354-362 :
    Perturbation Expansion for the Asymmetric Anderson Hamiltonian
    Kosaku Yamada
  50. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 595-607 :
    Ground State of the Asymmetric Anderson Model in the T-Matrix Approximation
    Hidetoshi Fukuyama and Akio Sakurai
  51. Progress of Theoretical Physics Vol. 62 No. 4 (1979) pp. 901-914 :
    Interaction between Localized Moments in Metals
    Kosaku Yamada
  52. Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1441-1457 :
    Ground State of the Asymmetric Anderson Model
    Satoru Inagaki
  53. Progress of Theoretical Physics Vol. 72 No. 3 (1984) pp. 402-411 :
    Superconductivity in the Dense Kondo System
    Tamifusa Matsuura, Kazumasa Miyake, Hisao Jichu and Yoshihiro Kuroda
  54. Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 621-638 :
    Fermi Liquid Theory on the Basis of the Periodic Anderson Hamiltonian
    Kosaku Yamada and Kei Yosida
  55. Progress of Theoretical Physics Vol. 128 No. 1 (2012) pp. 125-151 :
    Residual Entropy of the Mott Insulator with No Symmetry Broken
    Fusayoshi J. Ohkawa
  56. Progress of Theoretical Physics Supplement No.80 (1984) pp. 108-122 :
    Field Theoretical Approach to the Kondo Lattice Problem
    Tomio Koyama and Masashi Tachiki
  57. Progress of Theoretical Physics Supplement No.84 (1985) pp. 166-177 :
    Effects of Localization on Kondo Effect
    Fusayoshi J. Ohkawa
  58. Progress of Theoretical Physics Supplement No.106 (1991) pp. 95-107 :
    Heavy Electrons in the Mott-Transition Region
    Fusayoshi J. Ohkawa
  59. Progress of Theoretical Physics Supplement No.106 (1991) pp. 129-135 :
    Magnetic Ordering with Small Moments
    Kosaku Yamada and Satoru Inagaki
  60. Progress of Theoretical Physics Supplement No.108 (1992) pp. 73-88 :
    Excitation Spectra of the Impurity Anderson Model Calculated by the Numerical Renormalization Group Method
    Osamu Sakai, Yukihiro Shimizu and Tadao Kasuya
  61. Progress of Theoretical Physics Supplement No.108 (1992) pp. 209-228 :
    Magnetism in Heavy-Electron Liquids
    Fusayoshi J. Ohkawa
  62. Progress of Theoretical Physics Supplement No.108 (1992) pp. 251-263 :
    Exact Solution of Correlated Electron Systems
    Norio Kawakami and Ayao Okiji