Rich phase diagram of quantum phases in the anisotropic subohmic spin-boson model

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 gives an overall picture of the phase diagram. For small power of the spectral function of the bosonic bath, the quantum phase transition (QPT) from phase Ito III with mean-field critical behavior is present, similar to the isotropic SBM. The phase diagram with three different phases can be found at large power of the spectral function: For the highly anisotropic case, the system experiences the QPTs from phase Ito II via first order, and then to phase III via second order with the increase of the coupling strength. For the low anisotropic case, the system only experiences the continuous QPT from phase Ito 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 light-matter interacting systems. The present study on the anisotropic SBM could open an avenue to the rich quantum criticality.