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

Abstract

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.