  We study the anisotropic spin-boson model (SBM) with the subohmic bath by a
numerically exact method based on variational matrix product states. A rich
phase diagram is found in the anisotropy-coupling strength plane by calculating
several observables. There are three distinct quantum phases: a delocalized
phase with even parity (phase I), a delocalized phase with odd parity (phase
II), and a localized phase with broken $Z_2$ symmetry (phase III), which
intersect at a quantum tricritical point. The competition between those phases
would give overall picture of the phase diagram. For small power of the
spectral function of the bosonic bath, the quantum phase transition (QPT) from
phase I to III with mean-field critical behavior is present, similar to the
isotropic SBM. The novel phase diagram full with three different phases can be
found at large power of the spectral function: For highly anisotropic case, the
system experiences the QPTs from phase I to II via 1st-order, and then to the
phase III via 2nd-order with the increase of the coupling strength. For low
anisotropic case, the system only experiences the continuous QPT from phase I
to phase III with the non-mean-field critical exponents. Very interestingly, at
the moderate anisotropy, the system would display the continuous QPTs for
several times but with the same critical exponents. This unusual reentrance to
the same localized phase is discovered in the light-matter interacting systems.
The present study on the anisotropic SBM could open an avenue to the rich
quantum criticality.
