  Using large-scale dynamical cluster quantum Monte Carlo simulations, we study
the Lifshitz transition of the two dimensional Hubbard model with
next-nearest-neighbor hopping ($t'$), chemical potential and temperature as
control parameters. At $t'\le0$, we identify a line of Lifshitz transition
points associated with a change of the Fermi surface topology at zero
temperature. In the overdoped region, the Fermi surface is complete and
electron-like; across the Lifshitz transition, the Fermi surface becomes
hole-like and develops a pseudogap. At (or very close to) the Lifshitz
transition points, a van Hove singularity in the density of states crosses the
Fermi level. The van Hove singularity occurs at finite doping due to
correlation effects, and becomes more singular when $t'$ becomes more negative.
The resulting temperature dependence on the bare d-wave pairing susceptibility
close to the Lifshitz points is significantly different from that found in the
traditional van Hove scenarios. Such unambiguous numerical observation of the
Lifshitz transition at $t'\le0$ extends our understanding of the quantum
critical region in the phase diagram, and shines lights on future
investigations of the nature of the quantum critical point in the two
dimensional Hubbard model.
