Quantum criticality in sub-Ohmic systems with three competing terms: Beyond conventional spin-boson physics

Quantum phase transitions (QPTs) in the spin-boson model with/without the rotating-wave approximation (RWA) are systematically investigated through variational calculations using a sub-Ohmic bath with high spectral density. Four cases involving different system-environment interactions are examined, where transition points and critical exponents are accurately determined across varying tunneling strengths. Contrary to prior work, a rich phase diagram is revealed in the tunneling-coupling plane even at the low spectral exponent s<1/2, with a novel U (1) -symmetric phase being identified. As coupling increases, a multi-stage QPT sequence arises for the tunneling 0<Δ< Δ^*=0. 074 (1), whereas a single transition occurs beyond this range. Furthermore, an odd-parity phase is found to emerge even under the positive tunneling, exhibiting distinct characteristics relative to the prototype model.