One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ’Efimov physics’. The purpose of this presentation is to demonstrate the universality of this quantum phase transition for a class of systems with anisotropic scaling symmetry between space and time. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. We present experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene. We discuss the effect of spin to this transition and its relation to parity symmetry.