Probing Dark Matter Halos of High-redshift Quasars via Wide-Field Clustering
High-redshift quasars are powerful tracers of both astrophysical processes and large-scale structure in the early Universe. Using a sample of 1,251 spectroscopically confirmed quasars and 827 highly reliable photometric quasar candidates selected with a machine-learning framework, all at $4.7 \leq z < 6.3$ (excluding $5.4 < z < 5.6$) and with a median luminosity of $M_{1450}\sim -25.5$, we investigate the large-scale environments of quasars near the end of cosmic reionization. We measure the projected auto-correlation function of the quasar population and derive bias parameters of $b=22.11^{+2.17}_{-2.19}$ and $28.55^{+5.76}_{-5.75}$ for the redshift intervals $4.7\leq z<5.4$ and $5.6\leq z<6.3$, respectively. These correspond to characteristic dark matter halo masses of $\log(M_{ h}/M_\odot)=12.66^{+0.10}_{-0.11}$ and $12.62^{+0.21}_{-0.21}$, respectively. We further estimate quasar duty cycles of $0.011^{+0.017}_{-0.007}$ and $0.012^{+0.104}_{-0.011}$ for the two redshift bins. These measurements are consistent with previous studies and the observed $f_{\rm duty}$--$M_{\rm halo}$ relation, indicating that only a small fraction of suitable dark matter halos host optically luminous quasars at any given time. The inferred low duty cycles suggest that a substantial fraction of supermassive black hole growth may occur during obscured accretion phases. Our results provide new constraints on the connection between high-redshift quasars and their host dark matter halos, offering valuable insights into the co-evolution of supermassive black holes and large-scale structure in the early Universe.