Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions

Details Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions

2006-01-16

arxiv.org/abs/cond-mat/0601338v1

Int. J. of Mod. Phys. B, Vol. 20, No. 4, 381 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

Review article, 40 pages, 11 figures

Scientific paper

10.1142/S0217979206033310

We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means of imaginary Lagrange multipliers resulting in special shape of quasiparticle distribution functions. We show how Schwinger-Keldysh technique for spin operators is constructed with the help of semi-fermions. We demonstrate how the idea of semi-fermionic representation might be extended to the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in quantum dots). We illustrate the application of semi-fermionic representations for various problems of strongly correlated and mesoscopic physics.

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