  We summarize the recent developments in the model design and computation for
a few representative quantum many-body systems, encompassing quantum critical
metals beyond the Hertz-Millis-Moriya framework with pseudogap and
superconductivity, SYK non-Fermi-liquid with self-tuned quantum criticality and
fluctuation induced superconductivity, and the flat-band quantum Moir\'e
lattice models in continuum where the interplay of quantum geometry of
flat-band wave function and the long-range Coulomb interactions gives rise to
novel insulating phases at integer fillings and superconductivity away from
them. Although the narrative choreography seems simple, we show how important
the appropriate model design and their tailor-made algorithmic developments --
in other words, the scientific imagination inspired by the corresponding fast
experimental developments in the aforementioned systems -- compel us to invent
and discover new knowledge and insights in the sport and pastime of quantum
many-body research.
