The most generalized analytical approximation to the solution of single-mode spin-boson model without rotating-wave approximation

The single-mode spin-boson model (SMSBM) has extensive application in different subfields of physics. In the absence of rotating-wave approximation (RWA), we try to solve SMSBM analytically. We argue that the analytical expression obtained is the most exact approximation to the solution of the system under the assumption of Abel-Ruffini theorem, which works for a wide range of the parameters such as coupling strength and detuning and would be practical for currently available experiments.