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Geometrical and topological properties of quantum ground state manifoldspermits to characterize phases of matter, and identify phase transitions. Here,we study the effect of a quantum dissipative environment on the geometricalproperties of the ground state manifold of a single spin 1/2 in an externaleffective magnetic field. We show that the quantum phase transition at zerotemperature in the model is associated with a universal metric singularityrelated to the divergence of the spin susceptibility. The absence of transitionat finite temperature corresponds to a smooth variation of the associatedmetric with temperature, without singular points.

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