We present deep near-infrared spectroscopy of six quasars at 6.1<z<6.7 with VLT/X-Shooter and Gemini-N/GNIRS. Our objects, originally discovered through a wide-field optical survey with the Hyper Suprime-Cam (HSC) Subaru Strategic Program (HSC-SSP), have the lowest luminosities (-25.5< M1450<-23.1 mag) of the z>5.8 quasars with measured black hole masses. From single-epoch mass measurements based on MgII2798, we find a wide range in black hole masses, from M_BH=10^7.6 to 10^9.3 Msun. The Eddington ratios L_bol/L_Edd range from 0.16 to 1.1, but the majority of the HSC quasars are powered by M_BH=10^9 Msun supermassive black holes (SMBHs) accreting at sub-Eddington rates. The Eddington ratio distribution of the HSC quasars is inclined to lower accretion rates than those of Willott et al. (2010a), who measured the black hole masses for similarly faint z=6 quasars. This suggests that the global Eddington ratio distribution is wider than has previously been thought. The presence of M_BH=10^9 Msun SMBHs at z=6 cannot be explained with constant sub-Eddington accretion from stellar remnant seed black holes. Therefore, we may be witnessing the first buildup of the most massive black holes in the first billion years of the universe, the accretion activity of which is transforming from active growth to a quiescent phase. Measurements of a larger complete sample of z>6 low-luminosity quasars, as well as deeper observations with future facilities will enable us to better understand the early SMBH growth in the reionization epoch.
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