Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model

Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial quantum criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single S=1/2 spin where each spin component couples to an independent bosonic bath with power-law spectrum ˢ via dissipation strengths ᵢ, i\x, y, z\, such phenomena occur sequentially for the U (1) -symmetric model at ᵦ=0 and the SU (2) -symmetric case at ᵦ = ₗₘ, as the bath exponent s<1 is tuned. Here we use an exact wormhole quantum Monte Carlo method to show how fixed-point annihilations within symmetry-enhanced parameter manifolds affect the anisotropy-driven criticality across them. We find a tunable transition between two long-range-ordered localized phases that can be continuous or strongly first-order, and even becomes weakly first-order in an extended regime close to the fixed-point collision. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent s. In particular, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent. In addition, we also study the crossover behavior away from the SU (2) -symmetric case and determine the phase boundary of an extended U (1) -symmetric critical phase for ᵦ < ₗₘ.