  We study the stellar dynamics of the first star clusters after
intermediate-mass black holes (IMBHs) are formed via runaway stellar
collisions. We use the outputs of cosmological simulations of Sakurai et al.
(2017) to follow the star cluster evolution in a live dark matter (DM) halo.
Mass segregation within a cluster promotes massive stars to be captured by the
central IMBH occasionally, causing tidal disruption events (TDEs). We find that
the TDE rate scales with the IMBH mass as $\dot{N}_{\rm TDE}\sim0.3\,{\rm
Myr}^{-1}(M_{\rm IMBH}/1000\,{\rm M}_{\odot})^2$. The DM component affects the
star cluster evolution by stripping stars from the outer part. When the DM
density within the cluster increases, the velocity dispersion of the stars
increases, and then the TDE rate decreases. By the TDEs, the central IMBHs grow
to as massive as $700-2500\,{\rm M}_{\odot}$ in 15 million years. The IMBHs are
possible seeds for the formation of supermassive BHs observed at $z\gtrsim
6-7$, if a large amount of gas is supplied through galaxy mergers and/or
large-scale gas accretion, or they might remain as IMBHs from the early epochs
to the present-day Universe.
