Causality versus ward identity in disordered electron systems

Modern Physics Letters B

Volumn 18, Issue 19-20, 2004, Pages 1051-1058

  Janis V ^a   Kolorenc J ^a  

^a INSTITUTE OF MATHEMATICS   (Czech Republic)

Author keywords

Causality; Diffusion pole; Disordered electrons; Probability conservation; Ward identity

Indexed keywords

ARTICLE; DIFFUSION; ELECTRON; ENERGY; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR INTERACTION;

EID: 8644286137     PISSN: 02179849     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0217984904007591     Document Type: Article

References (13)

1. P. W. Anderson, Phys. Rev. 109 (1958) 1492.
2. M. L. Mehta, Random Matrices and Statistical Theory of Energy Levels (Academic Press, New York 1967).
3. R. J. Elliot, J. A. Krumhansl and P. L. Leath, Rev. Mod. Phys. 46 (1974) 465.
4. A. Gonis, Green Functions for Ordered and Disordered Systems (North Holland, Amsterdam, 1992).
5. D. Vollhardt and P. Wölfle, Phys. Rev. B22 (1980) 4666.
6. V. Janiš, Phys. Rev. B64 (2001) 115115.
7. D. Vollhardt and P. Wölfle, in Electronic Phase Transitions, eds. W. Hanke and Yu. V. Kopaev (Elsevier Science Publishers B. V., Amsterdam, 1992).
8. V. Janiš, J. Kolorenč and V. Špička, Eur. Phys. J. B35 (2003) 77.
9. Note that the CPA does contain the diffusion pole, but the electron-hole symmetry of the vertex functions is broken in this approximation.
10. R. Mills and P. Ratanavararaksa, Phys. Rev. B18 (1978) 5291; T. Kaplan, P. L. Leath, L. J. Gray and H. W. Diehl, ibid. B21 (1980) 4230.
11. R. Mills and P. Ratanavararaksa, Phys. Rev. B18 (1978) 5291; T. Kaplan, P. L. Leath, L. J. Gray and H. W. Diehl, ibid. B21 (1980) 4230.
12. There is no nonanalyticity and hence no violation of the Ward identity for imaginary energy differences Δz = 2iη in the electron-hole irreducible vertex.
13. Notice that the existing "nonperturbative" derivations of Ward identities in disordered systems apply only to single configurations of the random potential. The extension of the Ward identity to the averaged quantities is only intuitive and is based on a tacit assumption (not proved) that we can select a single Hilbert space (spanned by Bloch waves) encompassing almost all random configurations. See for example, R. Ramazashvili, Phys. Rev. B66 (2002) 220503.