Geometrical properties of the ground state manifold in the spin boson model

Geometrical and topological properties of quantum ground state manifolds permits to characterize phases of matter, and identify phase transitions. Here, we study the effect of a quantum dissipative environment on the geometrical properties of the ground state manifold of a single spin 1/2 in an external effective magnetic field. We show that the quantum phase transition at zero temperature in the model is associated with a universal metric singularity related to the divergence of the spin susceptibility. The absence of transition at finite temperature corresponds to a smooth variation of the associated metric with temperature, without singular points.