The Large-scale Environments of Low-luminosity AGNs at $3.9 < z < 6$ and Implications for Their Host Dark Matter Halos from a Complete NIRCam Grism Redshift Survey

We study the large-scale environments and clustering properties of 28 low-luminosity AGNs at $z=3.9-6$ in the GOODS-N field. Our sample, identified from the JWST NIRCam Imaging and WFSS data in CONGRESS and FRESCO surveys with either broad H$\alpha$ emission lines or V-shape continua, are compared to 782 H$\alpha$ emitters (HAEs) selected from the same data. These AGNs are located in diverse large-scale environments and do not preferentially reside in denser environments compared to HAEs. Their overdensity field, $\delta$, averaged over (15 $h^{-1}$cMpc)$^3$, ranges from $-0.56$ to 10.56, and shows no clear correlation with broad-line luminosity, black hole (BH) masses, or the AGN fraction. It suggests that $> 10$ cMpc structures do not significantly influence BH growth. We measure the two-point cross-correlation function of AGNs with HAEs, finding a comparable amplitude to that of the HAE auto-correlation. This indicates similar bias parameters and host dark matter halo masses for AGNs and HAEs. The correlation length of field AGNs is 4.26 $h^{-1}$cMpc, and 7.66 $h^{-1}$cMpc at $3.9 < z < 5$ and $5 < z < 6$, respectively. We infer a median host dark matter halo mass of $\log (M_h/M_\odot)\approx 11.0-11.2$ and host stellar masses of $\log (M_\star/M_\odot) \approx 8.4-8.6$ by comparing with the UniverseMachine simulation. Our clustering analysis suggests that low-luminosity AGNs at high redshift reside in normal star-forming galaxies with overmassive BHs. They represent an intrinsically distinct population from luminous quasars and could be a common phase in galaxy evolution.