  The halon is a special critical state of an impurity in a quantum-critical
environment. The hallmark of the halon physics is that a well-defined integer
charge gets fractionalized into two parts: a microscopic core with half-integer
charge and a critically large halo carrying a complementary charge of $\pm
1/2$. The halon phenomenon emerges when the impurity--environment interaction
is fine-tuned to the vicinity of a boundary quantum critical point (BQCP), at
which the energies of two quasiparticle states with adjacent integer charges
approach each other. The universality class of such BQCP is captured by a model
of pseudo-spin-$1/2$ impurity coupled to the quantum-critical environment, in
such a way that the rotational symmetry in the pseudo-spin $xy$-plane is
respected, with a small local "magnetic" field along the pseudo-spin $z$-axis
playing the role of control parameter driving the system away from the BQCP. On
the approach to BQCP, the half-integer projection of the pseudo-spin on its
$z$-axis gets delocalized into a halo of critically divergent radius, capturing
the essence of the phenomenon of charge fractionalization. With large-scale
Monte Carlo simulations, we confirm the existence of halons---and quantify
their universal features---in O(2) and O(3) quantum critical systems.
