Gauge principle and gauge invariance in two-level systems

The quantum Rabi model is a widespread description for the coupling between two-level system and quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when light-matter interaction reaches so-called ultrastrong regime. Recently, modified able to provide gauge-invariant physical results in any regime was introduced [Nature Physics 15, 803 (2019)]. Here we alternative derivation result, based on implementation two-state systems principle, which principle from all fundamental interactions field theory are derived. adopted procedure can be regarded as two-site version general method used implement lattice theories. Applying method, also obtain asymmetric systems, multi-mode beyond dipole approximation.