  How do protons and neutrons bind to form nuclei? This is the central question
of ab initio nuclear structure theory. While the answer may seem as simple as
the fact that nuclear forces are attractive, the full story is more complex and
interesting. In this work we present numerical evidence from ab initio lattice
simulations showing that nature is near a quantum phase transition, a
zero-temperature transition driven by quantum fluctuations. Using lattice
effective field theory, we perform Monte Carlo simulations for systems with up
to twenty nucleons. For even and equal numbers of protons and neutrons, we
discover a first-order transition at zero temperature from a Bose-condensed gas
of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an
alpha-particle gas or nuclear liquid is determined by the strength of the
alpha-alpha interactions, and we show that the alpha-alpha interactions depend
on the strength and locality of the nucleon-nucleon interactions. This insight
should be useful in improving calculations of nuclear structure and important
astrophysical reactions involving alpha capture on nuclei. Our findings also
provide a tool to probe the structure of alpha cluster states such as the Hoyle
state responsible for the production of carbon in red giant stars and point to
a connection between nuclear states and the universal physics of bosons at
large scattering length.
