Emergent electromagnetism in solids

The electromagnetic field (EMF) is the most fundamental field in condensed-matter physics. Interaction between electrons, electron-ion interaction and ion-ion interaction are all of electromagnetic origin, while the other three fundamental forces, i.e. the gravitational force and weak and strong interactions, are irrelevant in the energy/length scales of condensed-matter physics. Also the physical properties of condensed matter, such as transport, optical, magnetic and dielectric properties, are almost described as their electromagnetic responses. In addition to this EMF, it often happens that the gauge fields appear as the emergent phenomenon in the low-energy sector due to the projection of the electronic wavefunctions onto the curved manifold of the Hilbert sub-space. These emergent EMFs play important roles in many places in condensed-matter physics including the quantum Hall effect, strongly correlated electrons and also in non-interacting electron systems. In this paper, we describe the fundamental idea behind it and some of its applications studied recently.