  In the vicinity of continuous quantum phase transitions (QPTs), quantum
systems become scale-invariant and can be grouped into universality classes
characterized by sets of critical exponents. We have found that despite
scale-invariance and universality, the experimental data still contain
information related to the microscopic processes and scales governing QPTs. We
have found that for many systems, the scaled data near QPTs can be approximated
by the generic exponential dependence introduced in the scaling theory of
localization; this dependence includes as a parameter a microscopic seeding
scale of the renormalization group, $L_0$. We have also conjectured that for
interacting systems, the temperature cuts the renormalization group flow at the
length travelled by a system-specific elementary excitation over the life-time
set by the Planckian time, $\tau_P$=$\hbar/k_BT$. We have adapted this approach
for QPTs in several systems and showed that $L_0$ extracted from experiment is
comparable to physically-expected minimal length scales, namely (i) the mean
free path for metal-insulator transition in doped semiconductor Si:B, (ii) the
distance between spins in Heisenberg and Ising chains, (iii) the period of an
optical lattice for cold atom boson gases, and (iv) the period of a moir\'e
superlattice for the Mott QPT in dichalcogenide bilayers. The metal-insulator
transition in Si:P has been explained using a non-interacting version of the
model. In two companion papers, we show that in superconducting systems, $L_0$
is comparable to superconducting coherence length, and in quantum Hall systems,
to the magnetic length. The developed new method of data analysis identifies
microscopic processes leading to QPTs and quantitatively explains and unifies a
large body of experimental data.
