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

TL;DR

This paper develops a semi-fermionic representation for spin operators using fermionic bilinears, applicable in equilibrium and non-equilibrium conditions, with potential extensions to dynamic symmetry groups and applications in strongly correlated systems.

Contribution

It introduces a general derivation of semi-fermionic representation for spins, incorporating imaginary Lagrange multipliers and extending the Schwinger-Keldysh technique for non-equilibrium analysis.

Findings

Derived semi-fermionic representation for spin operators.

Constructed Schwinger-Keldysh formalism with semi-fermions.

Applied method to strongly correlated and mesoscopic physics problems.

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.