Semi-Fermionic Representation for Spin Systems Under Equilibrium and Non-Equilibrium Conditions

Abstract

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.

Decoherence and dephasing in Kondo tunneling through double quantum dots

“…The adiabatic contribution of a charge transfer exciton (E) to the effective indirect exchange (cotunneling) Hamiltonian may be taken into account by means of a time dependent Schrieffer-Wolff transformation, which includes H tun (t) (22). This transformation is described in Ref.…”

“…(25) The coefficients υ Λ k are chosen to eliminate the time dependent terms (22) in the effective Hamiltonian…”

Tunneling and magnetic properties of triple quantum dots

“…Various manifestations of dynamical symmetries in physical problems are described in the monongraphs [45,46]. Some mathematical aspects of the dynamical symmetries as applied to the Kondo problem may be found in the recent reviews [47,48].…”

“…The algebra o 7 contains 21 generator for the group SO( ) 7 . These are two spin vectors S S tails in the reviews [47,48] and in the thesis [55]. Casimir constraint for SO n ( ) group has the form…”

Dynamical symmetries and quantum transport through nanostructures

“…The methods implemented for a weak-coupling Kondo regime in [8] are not applicable for the quantitative and even qualitative description of nonequilibrium effects (full nonlinearconductance etc) at large biases eV ∆. The kinetic equation approach based on Schwinger-Keldysh diagrammatics [9,10] might be appropriate tool to describe the regime of strong out of equilibrium in double quantum dots.…”