Generalization, order, and cross-correlated physical characteristics of microscopic multipoles

This paper introduces that by introducing four generalized multipoles with different parity in space-time, namely electric dipole, magnetic dipole, electric toroidal dipole, and magnetic toroidal dipole, it is possible to describe all electronic degrees of freedom. In addition, the four types of multipoles are closely related to the components of the physical tensor that characterizes various physical responses, and are suitable to describe off-diagonal responses (cross-correlated responses) with different parity regarding the space-time inversion of inputs and outputs. This paper introduces these facts by referring to the electromagnetic effect as an example. Furthermore, it takes up the cluster multipoles that are activated by expanding the state space to multiple atoms and the bond multipoles that were obtained by classifying, according to symmetry, the hopping modulation degree of freedom that are the basis of the bond ordering, and introduces the outline and application examples of them. (A.O.)