Abstract
We discuss the functional integral approach to the magnetic impurity using the symmetric two-variable method. Namely, we avoid using the identityn 2=n for the localized state. We show that this procedure has clear advantages over all other linearizations of the Coulomb interaction in the Anderson Hamiltonian: it satisfies the symmetry with respect to the change of sign ofU in all approximations; it gives the first corrections to the nonmagnetic and magnetic limits already in the static approximation; it allows representation, both in the static approximation and in higher ones, of the partition function as an average overd-state occupation numbers; and calculations are much simplified. We present numerical calculations of the susceptibility for comparison of the results of the two-variable method to Hamann's saddle-point procedure or to the equivalent one-variable approach.
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References
C. Herring,Magnetism, G. T. Rado and H. Suhl, eds. (New York, Academic Press, 1966), Vol. 4.
P. W. Anderson,Phys. Rev. 124, 41 (1961).
N. Rivier, M. Sunjic, and M. J. Zuckermann,Phys. Letters 28A, 492 (1968).
M. T. Beal-Monod and D. L. Mills,Phys. Rev. Letters 24, 225 (1970).
D. J. Scalapino,Phys. Rev. Letters 16, 937 (1966).
H. Keiter and J. C. Kimball,Intern J. Magnetism 1, 233 (1971).
B. Muhlschlegel, unpublished lecture notes, University of Pennsylvania, 1965.
S. Q. Wang, W. E. Evenson, and J. R. Schrieffer,Phys. Rev. Letters 23, 92 (1969).
D. R. Hamann,Phys. Rev. Letters 23, 95 (1969);Phys. Rev. B2, 1373 (1970).
H. Keiter,Phys. Rev. B2, 3777 (1970).
K. Yosida and K. Yamada,Suppl. Progr. Theoret. Phys. 46, 244 (1971).
G. Iche and A. Zawadowsky,Solid State Commun. 10, 1001 (1972).
H. Keiter and A. Theumann,Solid State Commun. 11, 811 (1972).
D. J. Amit and C. M. Bender,Phys. Rev. B4, 3115 (1971).
R. L. Stratonovich,Dokl. Akad. Nauk SSSR 115, 1097 (1957) [English transl.,Soviet Phys.—Doklady 2, 416 (1958)]; J. Hubbard,Phys. Rev. Letters 3, 77 (1958).
Au. A. Byckov, L. P. Gor'kov, and I. E. Dzyaloshinskii,Soviet Phys.—JETP 23, 489 (1966).
B. Roulet, J. Gavoret, and P. Nozieres,Phys. Rev. 178, 1072, 1084 (1969).
Higher Transcendental Functions I, Bateman manuscript project (McGraw-Hill, New York, 1953), Eq. 30, p. 12.
R. F. Hassing and D. M. Esterling, Indiana University preprint, 1972.
R. A. Bari,Phys. Rev. B5, 2736 (1972).
B. Muhlsehlegel and E. Muller-Hartmann, 1967, unpublished.
G. N. Watson,A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge, 1966).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1965), p. 256.
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Amit, D.J., Keiter, H. Functional integral approach to the magnetic impurity problem: The superiority of the two-variable method. J Low Temp Phys 11, 603–622 (1973). https://doi.org/10.1007/BF00654449
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DOI: https://doi.org/10.1007/BF00654449