  By employing the spin-boson model in a dense limit of environmental modes,
quantum entanglement and correlation of sub-Ohmic and Ohmic baths for
dissipative quantum phase transitions are numerically investigated based on the
variational principle. With several measures borrowed from quantum information
theory, three different types of singularities are found for the first-order,
second-order, and Kosterlitz-Thouless phase transitions, respectively, and the
values of transition points and critical exponents are accurately determined.
Besides, the scaling form of the quantum discord in the Ohmic case is
identified, quite different from that in the sub-Ohmic regime. In a two-spin
model, two distinct behaviors of the quantum discord are uncovered: one is
related to the quantum entanglement between two spins and the other is decided
by the correlation function in the position space rather than the entanglement.
