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.

Review article, 40 pages, 11 figures

References in corpus (6)

• Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
• Kondo effect in systems with dynamical symmetries
• Spin Gap in Chains with Hidden Symmetries
• Dynamical symmetries in nanophysics
• Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature
• Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State

Cited by in corpus (8)

• Heavy-fermion valence-bond liquids in ultracold atoms: Cooperation of Kondo effect and geometric frustration
• From Popov-Fedotov trick to universal fermionization
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Decoherence and Dephasing in Kondo Tunneling through Double Quantum Dots
• Grassmannization of classical models
• Orbital order and Hund's rule frustration in Kondo lattices
• Kondo effect in Complex Quantum Dots in the presence of an oscillating and fluctuating gate signal
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism