Constraining the Hubble constant to a precision of about 1% using
  multi-band dark standard siren detections
  Gravitational wave signal from the inspiral of stellar-mass binary black hole
can be used as standard sirens to perform cosmological inference. This inspiral
covers a wide range of frequency bands, from the millihertz band to the
audio-band, allowing for detections by both space-borne and ground-based
gravitational wave detectors. In this work, we conduct a comprehensive study on
the ability to constrain the Hubble constant using the dark standard sirens, or
gravitational wave events that lack electromagnetic counterparts. To acquire
the redshift information, we weight the galaxies within the localization error
box with photometric information from several bands and use them as a proxy for
the binary black hole redshift. We discover that TianQin is expected to
constrain the Hubble constant to a precision of roughly $30\%$ through
detections of $10$ gravitational wave events; in the most optimistic case, the
Hubble constant can be constrained to a precision of $< 10 \%$, assuming
TianQin I+II. In the optimistic case, the multi-detector network of TianQin and
LISA is capable of constraining the Hubble constant to within $5\%$ precision.
It is worth highlighting that the multi-band network of TianQin and Einstein
Telescope is capable of constraining the Hubble constant to a precision of
about $1\%$. We conclude that inferring the Hubble constant without bias from
photo-z galaxy catalog is achievable, and we also demonstrate self-consistency
using the P$-$P plot. On the other hand, high-quality spectroscopic redshift
information is crucial for improving the estimation precision of Hubble
constant.
