GOLDRUSH. II. Clustering of Galaxies at $z\sim 4-6$ Revealed with the Half-Million Dropouts Over the 100 deg$^2$ Area Corresponding to 1 Gpc$^3$

We present clustering properties from 579,492 Lyman break galaxies (LBGs) at z~4-6 over the 100 deg^2 sky (corresponding to a 1.4 Gpc^3 volume) identified in early data of the Hyper Suprime-Cam (HSC) Subaru strategic program survey. We derive angular correlation functions (ACFs) of the HSC LBGs with unprecedentedly high statistical accuracies at z~4-6, and compare them with the halo occupation distribution (HOD) models. We clearly identify significant ACF excesses in 10"<$\theta$<90", the transition scale between 1- and 2-halo terms, suggestive of the existence of the non-linear halo bias effect. Combining the HOD models and previous clustering measurements of faint LBGs at z~4-7, we investigate dark-matter halo mass (Mh) of the z~4-7 LBGs and its correlation with various physical properties including the star-formation rate (SFR), the stellar-to-halo mass ratio (SHMR), and the dark matter accretion rate (dotMh) over a wide-mass range of Mh/M$_\odot$=4x10^10-4x10^12. We find that the SHMR increases from z~4 to 7 by a factor of ~4 at Mh~1x10^11 M$_\odot$, while the SHMR shows no strong evolution in the similar redshift range at Mh~1x10^12 M$_\odot$. Interestingly, we identify a tight relation of SFR/dotMh-Mh showing no significant evolution beyond 0.15 dex in this wide-mass range over z~4-7. This weak evolution suggests that the SFR/dotMh-Mh relation is a fundamental relation in high-redshift galaxy formation whose star formation activities are regulated by the dark matter mass assembly. Assuming this fundamental relation, we calculate the cosmic SFR densities (SFRDs) over z=0-10 (a.k.a. Madau-Lilly plot). The cosmic SFRD evolution based on the fundamental relation agrees with the one obtained by observations, suggesting that the cosmic SFRD increase from z~10 to 4-2 (decrease from z~4-2 to 0) is mainly driven by the increase of the halo abundance (the decrease of the accretion rate).