The Halon: A Quasiparticle Featuring Critical Charge Fractionalization

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 ±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.