Critical and Strong-Coupling Phases in One- and Two-Bath Spin-Boson Models

For phase transitions in dissipative quantum impurity models, the existence of a quantum-to-classical correspondence has been discussed extensively. We introduce a variational matrix product state approach involving an optimized boson basis, rendering possible high-accuracy numerical studies across the entire phase diagram. For the sub-Ohmic spin-boson model with a power-law bath spectrum proportional to omega(s), we confirm classical mean-field behavior for s < 1/2, correcting earlier numerical renormalization-group results. We also provide the first results for an XY-symmetric model of a spin coupled to two competing bosonic baths, where we find a rich phase diagram, including both critical and strong-coupling phases for s < 1, different from that of classical spin chains. This illustrates that symmetries are decisive for whether or not a quantum-to-classical correspondence exists.