  A quantum phase transition (QPT) between distinct ground states of matter is
a wide-spread phenomenon in nature, yet there are only a few experimentally
accessible systems where the microscopic mechanism of the transition can be
tested and understood. These cases are unique and form the experimentally
established foundation for our understanding of quantum critical phenomena.
Here we report the discovery that a magnetic-field-driven QPT in
superconducting nanowires - a prototypical 1d-system - can be fully explained
by the critical theory of pair-breaking transitions characterized by a
correlation length exponent $\nu \approx 1$ and dynamic critical exponent $z
\approx 2$. We find that in the quantum critical regime, the electrical
conductivity is in agreement with a theoretically predicted scaling function
and, moreover, that the theory quantitatively describes the dependence of
conductivity on the critical temperature, field magnitude and orientation,
nanowire cross sectional area, and microscopic parameters of the nanowire
material. At the critical field, the conductivity follows a $T^{(d-2)/z}$
dependence predicted by phenomenological scaling theories and more recently
obtained within a holographic framework. Our work uncovers the microscopic
processes governing the transition: The pair-breaking effect of the magnetic
field on interacting Cooper pairs overdamped by their coupling to electronic
degrees of freedom. It also reveals the universal character of continuous
quantum phase transitions.
