Bosonization in the two-channel Kondo model

Physical Review B - Condensed Matter and Materials Physics

Volumn 55, Issue 9, 1997, Pages 5627-5630

  Schofield, A ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001464745     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.55.5627     Document Type: Article

References (22)

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16. At first sight, the coefficients obtained in Ref. 8 differ from those obtained here. However, this difference is an artifact of the regularization scheme [see F. Guinea, V. Hakim and A. Muramatsu, Phys. Rev. B 32, 4410 (1985), and references therein]. In bosonizing as above, a scattering phase shift is related to the scattering potential by (Formula presented)=V/4π(Formula presented) in contrast to (Formula presented)=(Formula presented)V/4π(Formula presented) of the x-ray edge problem. Thus by expressing Eq. (24) in terms of the physical phase shifts I obtain the same coefficients as in Ref. 8. For example, the Toulouse point here (J-(Formula presented)=2π(Formula presented), δ(Formula presented)=0) expressed in phase shifts implies (Formula presented)+(Formula presented)=π/2, (Formula presented)=(Formula presented). I am grateful to Qimiao Si for drawing my attention to this point.
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18. In comparing the finite-size spectra one needs to be careful to satisfy the "gluing conditions" [see, for example, I. Affleck, Acta Phys. Pol. B 26, 1869 (1995)] which couple the zero modes of the spin and charge channels in the (σ,τ) model: ((Formula presented),(Formula presented))\ must all be integer or all half-integer. This can be achieved at the noninteracting level since the interactions commute with this constraint. I thank Jan von Delft for pointing this out.
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