Phase and equation of state of finite density QC${}_2$D at lower temperature

We investigate the phase structure and the equation of state (EoS) for dense two-color QCD at low temperatures, $T=40$ MeV (${32}^4$ lattice) and $T=80$ MeV (${16}^4$ lattice). A rich phase structure below the pseudo-critical temperature $T_c$ as a function of quark chemical potential $\mu$ has been revealed. By performing $T=40$ MeV simulations, essentially similar results to the previous ones at $T=80$ MeV are obtained, but several finer understandings are achieved. Breaking of the conformal bound is also confirmed thanks to smaller statistical errors. This talk is mainly based on Refs.~\cite{Iida:2022hyy, Iida:2024irv}. It also includes related studies and subsequent developments that were not mentioned in the original papers.