A unified framework for the Kondo problem and for an impurity in a Luttinger liquid

Journal Article · Tue Oct 01 04:00:00 EDT 1996 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02175563· OSTI ID:468378

Fendley, P; Lesage, F; Saleur, H ^[1]

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1. Univ. of Southern California, Los Angeles, CA (United States)

We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values, respectively, in standard or cyclic representations of the quantum group SU(2){sub q}. This unification is powerful, and allows us to find new results for both models. For the anisotropic Kondo problem, we find exact expressions (in the presence of a magnetic field) for all the coefficients in the Anderson-Yuval perturbative expansion. Our expressions hold initially in the very anisotropic regime, but we show how to continue them beyond the Toulouse point all the way to the isotropic point using an analog of dimensional regularization. The analytic structure is transparent, involving only simple poles which we determine exactly, together with their residues. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the non-equilibrium conductance for all values of the Luttinger coupling. This is an intricate computation because the voltage operator and the boundary scattering do not commute with each other.

• Sponsoring Organization: USDOE
• OSTI ID: 468378
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 85; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
FERMI GAS
HAMILTONIANS
IMPURITIES
KONDO EFFECT
PARTITION FUNCTIONS
QUANTUM FIELD THEORY
QUANTUM FLUIDS
SINE-GORDON EQUATION