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Article

Semion formalism for spin and qubit systems: Non-Markovian treatment

Physical Review A: Atomic, Molecular, and Optical physics. 2020. Vol. 102. No. 4. P. 042224-1-042224-13.
Elistratov A. A., Remizov S. V., Yurii Lozovik.

Using semion substitution for spin variables we perform an ab initio derivation of effective action for an open quantum two-level system. For this purpose, we introduce, by using the Hubbard-Stratonovich transformation a two-time complex quantum field which average value plays the role of the Green's function for the spin variables. The field thus introduced allows us to develop a diagram technique in a standard way. The proposed formalism is used to study a spin embedded into an Ohmic reservoir as an example of the spin-boson model. Non-Markovian effects in this system are analyzed.