Exact conformal field theory results on the multichannel Kondo effect: Asymptotic three-dimensional space and time dependent multipoint and many particle Green's functions

Ludwig, A.W.W.; Affleck, I.

doi:10.1016/0550-3213(94)90365-4

Exact conformal field theory results on the multichannel Kondo effect: Asymptotic three-dimensional space and time dependent multipoint and many particle Green's functions

A.W.W. Ludwig
(
- Princeton U.
)
,
I. Affleck
(
- British Columbia U.
)

1994

67 pages

Published in:

Nucl.Phys.B 428 (1994) 545-611

DOI:

10.1016/0550-3213(94)90365-4

View in:

AMS MathSciNet

reference search53 citations

Citations per year

Abstract: (Elsevier)

We have recently developed a conformal field theory approach for quantum impurity problems, which include the multi-channel Kondo effect, allowing us to obtain exact asymptotic Green's functions, amongst other results. The single-fermion Green's function was presented in a separate publication. Here we present the detailed derivation of and explicit expressions for the four-point single-particle and two-point two-particle Green's functions, including the spin-density, charge-density and pair field Green's function. These represent universal crossover functions, from non-interacting (Fermi-liquid) behavior when all operators are far from the impurity, to singular (non-Fermi-liquid) behavior, characterized by Wess-Zumino-Witten conformal field theories, when operators move close to the impurity. These crossover functions show explicitly how “deconfinement” of the spin degrees of freedom near the impurity site occurs. The results are obtained for the general case of an SU( N ) impurity spin and k channels, using the Fusion Rule of Kac-Moody conformal field theory, modular transformations, the Verlinde formula, and Braid and Fusion matrices. We also show how to compute exact higher multi-point functions with our approach. From the four-point single-particle function we extract an operator product coefficient, needed for the computation of the resistivity. We also present the result for the Wilson ratio for an SU( N ) impurity spin.

field theory: conformal
n-point function
asymptotic expansion
algebra: Kac-Moody
symmetry: SU(N)
model: spin
spin: model
Kondo effect
Wess-Zumino-Witten model
bibliography

References(66)

Figures(0)

[1]

A Current Algebra Approach to the Kondo Effect

Ian Affleck
(
- Rutgers U., Piscataway and
- British Columbia U.
)

- Nucl.Phys.B 336 (1990) 517-532
•
DOI:
- 10.1016/0550-3213(90)90440-O

[2]

The Kondo effect, conformal field theory and fusion rules

- Nucl.Phys.B 352 (1991) 849-862
•
DOI:
- 10.1016/0550-3213(91)90109-B

[3]

Critical theory of overscreened Kondo fixed points

- Nucl.Phys.B 360 (1991) 641-696
•
DOI:
- 10.1016/0550-3213(91)90419-X

[4]

Universal noninteger 'ground state degeneracy' in critical quantum systems

- Phys.Rev.Lett. 67 (1991) 161-164
•
DOI:
- 10.1103/PhysRevLett.67.161

[5]

Exact asymptotic three-dimensional, space and time dependent Green's functions in the multichannel Kondo effect

Andreas W.W. Ludwig
(
- Simon Fraser U. and
- Saclay
)
,
Ian Affleck
(
- British Columbia U.
)

- Phys.Rev.Lett. 67 (1991) 3160-3163
•
DOI:
- 10.1103/PhysRevLett.67.3160

[6]

Exact critical theory of the two impurity Kondo model

Ian Affleck
(
- British Columbia U.
)
,
Andreas W.W. Ludwig
(
- British Columbia U. and
- Simon Fraser U.
)

- Phys.Rev.Lett. 68 (1992) 1046-1049
•
DOI:
- 10.1103/PhysRevLett.68.1046

[7]

Relevance of anisotropy in the multichannel Kondo effect: Comparison of conformal field theory and numerical renormalization group results

Ian Affleck
(
- British Columbia U.
)
,
Andreas W.W. Ludwig
(
- British Columbia U. and
- Simon Fraser U.
)
,
H.B. Pang
(
- Ohio State U.
)
,
D.L. Cox
(
- Ohio State U.
)

- Phys.Rev.B 45 (1992) 7918-7935
•
DOI:
- 10.1103/PhysRevB.45.7918

[8]

Field theory approach to critical quantum impurity problems and applications to the multichannel Kondo effect

A.W.W. Ludwig
(
- Simon Fraser U. and
- British Columbia U.
)

- Int.J.Mod.Phys.B 8 (1994) 347-402
•
DOI:
- 10.1142/S0217979294000130

[9]

Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green’s function, self-energy, and resistivity

Ian Affleck
(
- British Columbia U.
)
,
Andreas W.W. Ludwig
(
- British Columbia U. and
- Simon Fraser U.
)

- Phys.Rev.B 48 (1993) 10, 7297
•
DOI:
- 10.1103/PhysRevB.48.7297

[10]

Proceedings ofTrieste Summer School on Quantum Field Theory and Condensed Matter Physics (World Scientific, to be published)

A.W.W. Ludwig

[11]

P. Nozières
,
A. Blandin

- J.de Physique (Paris) 41 (1980) 193

[12]

P. Nozières

- J.Low Temp.Phys. 17 (1974) 31

[13]

P.W. Anderson
,
G. Yuval
,
D.R. Hamman

- Phys.Rev.B 1 (1970) 4464

[14]

The Renormalization Group: Critical Phenomena and the Kondo Problem

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Rev.Mod.Phys. 47 (1975) 773
•
DOI:
- 10.1103/RevModPhys.47.773

[15]

Solution of the Multichannel Kondo Problem

N. Andrei
(
- Rutgers U., Piscataway
)
,
C. Destri
(
- Rutgers U., Piscataway
)

- Phys.Rev.Lett. 52 (1984) 364-367
•
DOI:
- 10.1103/PhysRevLett.52.364

[16]

P.B. Wiegmann
,
A.M. Tsvelik

- Pis'ma Zh.Exp.Teor.Fiz. 38 (1983) 489

[17]

Bosonization of the Kondo Problem

Eduardo H. Fradkin
(
- Illinois U., Urbana and
- La Plata U.
)
,
C. Von Reichenbach
(
- Illinois U., Urbana and
- La Plata U.
)
,
F.A. Schaposnik
(
- Illinois U., Urbana and
- La Plata U.
)

- Nucl.Phys.B 316 (1989) 710-734
•
DOI:
- 10.1016/0550-3213(89)90065-5

[17]

Conformal properties of the Kondo models

- Nucl.Phys.B 340 (1990) 692-702
•
DOI:
- 10.1016/0550-3213(90)90464-O

[18]

A.M. Tsvelik

- J.Phys.Condens.Matter 2 (1990) 2833

[19]

Conformal Invariance and Surface Critical Behavior

John L. Cardy
(
- Boston U.
)

- Nucl.Phys.B 240 (1984) 514-532
•
DOI:
- 10.1016/0550-3213(84)90241-4

[20]

Boundary Conditions, Fusion Rules and the Verlinde Formula

John L. Cardy
(
- UC, Santa Barbara
)

- Nucl.Phys.B 324 (1989) 581-596
•
DOI:
- 10.1016/0550-3213(89)90521-X

[21]

Current Algebra and Wess-Zumino Model in Two-Dimensions

V.G. Knizhnik
(
- Moscow, ITEP
)
,
A.B. Zamolodchikov
(
- Moscow, ITEP
)

- Nucl.Phys.B 247 (1984) 83-103,
- Also in *Goddard, P. (ed.), Olive, D. (ed.): Kac-Moody and Virasoro algebras* 501-521, and in *Itzykson, C. (ed.) et al.: Conformal invariance and applications to statistical mechanics* 76-96,
•
DOI:
- 10.1016/0550-3213(84)90374-2

[22]

Luttinger liquid theory of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas

F.D.M. Haldane
(
- Laue-Langevin Inst.
)

- J.Phys.C 14 (1981) 2585-2609
•
DOI:
- 10.1088/0022-3719/14/19/010

[23]

C.L. Seaman

- Phys.Rev.Lett. 67 (1991) 2882

[24]

D.L. Cox

- Phys.Rev.Lett. 59 (1987) 1240

1-25 of 66
1
2
3
25 / page