  We investigate a spin-boson model with two boson baths that are coupled to
two perpendicular components of the spin by employing the density matrix
renormalization group method with an optimized boson basis. It is revealed that
in the deep sub-Ohmic regime there exists a novel second-order phase transition
between two types of doubly degenerate states, which is reduced to one of the
usual type for nonzero tunneling. In addition, it is found that expectation
values of the spin components display jumps at the phase boundary in the
absence of bias and tunneling.
