  Electronic modes emerge within the band gap at nonzero temperature in
strongly correlated insulators such as Mott and Kondo insulators, exhibiting
momentum-shifted magnetic dispersion relations from the band edges. As the
temperature increases, the emergent modes gain considerable spectral weights
and form robust bands that differ from the zero-temperature bands. Here, the
origin of the emergent modes, their relation to doping-induced modes, and how
their spectral weights increase with temperature are clarified in the ladder
and bilayer Hubbard models and one- and two-dimensional Kondo lattice models
using effective theory for weak inter-unit-cell hopping and numerical
calculations. The results indicate that the temperature-driven change in the
band structure reflecting spin excitation, including the change in the number
of bands, can be observed in various strongly correlated insulators even with a
spin gap, provided that the temperature increases up to about spin-excitation
energies. The controlled analyses developed in this study significantly
contribute to the fundamental understanding of the band structure of strongly
correlated insulators at nonzero temperature.
