Light-matter interaction in the long-wavelength limit: necessity of the dipole self-energy.

Most theoretical studies for correlated light-matter systems are performed within the long-wavelength limit, i.e., the electromagnetic field is assumed to be spatially uniform. In this limit the so-called length-gauge transformation for a fully quantized light-matter system gives rise to the dipole self-energy of the electrons. In practice this term is often discarded as it is assumed to be subsumed in the kinetic energy term. In this presentation we show the necessity of the dipole self-energy term. First and foremost, without it the light-matter system in the long-wavelength limit does not have a ground-state. Further implications of the dipole self-energy will be presented, such as the change of the translation operator and how this influences the Bloch theorem.