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