  We present an analytic theory unraveling the microscopic mechanism of
instabilities within interacting $D$-dimensional Fermi liquid. Our model
consists of a $D$-dimensional electron gas subject to an instantaneous
electron-electron interaction of a finite range exceeding the average
inter-particle distance. Pair, charge and spin susceptibilities are evaluated
via the one-loop renormalization group theory and via the bosonization
approach, giving identical results. In case of a repulsive interaction, we
identify an intrinsic Fermi liquid instability towards insulating spin/charge
density wave order when the interaction coupling strength reaches a universal
critical value. If both electron and hole pockets of the same size are present,
the ground state is an excitonic insulator at arbitrarily small repulsive
interaction. If the interaction is attractive, the ground state is a singlet
non-BCS superconductor with a uniform condensate. In case if both electron and
hole Fermi surfaces are present, we predict an instability towards the
inter-pocket pair-density-wave ordering at the critical coupling. This
prediction lends strong theoretical support to the pair-density-wave scenario
of superconductivity in cuprate materials. Due to its simple and universal
nature, presented microscopic mechanism of intrinsic instabilities of
interacting $D$-dimensional Fermi liquids constitutes a solid theoretical
ground for understanding quantum phase transitions in a variety of quantum
materials, from ultraclean semiconductor quantum wells to high-temperature
superconductors.
