Rich quantum phases in the anisotropic sub-Ohmic spin-boson model.

We study the anisotropic spin-boson model (SBM) by a numerically exact method based on variational matrix product states. Rich phase diagram is found in the anisotropy-coupling strength plane by calculating several observables. There are three distinct quantum phases: delocalized phase with even parity (phase I), delocalized phase with odd parity (phase II), and localized phase with broken $Z_2$ symmetry (phase III), which intersect at a quantum tricritical point. The competition between those phases will give overall picture of the phase diagram. For small bath exponent in the regime of $s 1/2$: For highly anisotropic case, the system will undergo the QPTs from phase I to II via 1st-order, and then to the phase III via 2nd-order with 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 first discovered in the light-matter interacting systems. Thus, the anisotropic SBM would be potential interesting platform to study the rich quantum criticality.