Irrational vs. rational charge and statistics in two-dimensional quantum systems

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-biding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge re-rationalizes to the value 1/2 and the exchange statistics to that of “quartons” (half-semions).