The Order Fractionalization Hypothesis: Applications to Heavy Electron and Strongly Correlated Materials

Landau's theory of phase transitions places no à priori constraint on the microscopic nature of broken symmetry, but in electronic systems we generally assume that an order parameter involves an even number of electrons or holes: the basis of the Hartree-Fock, BCS paradigm. The Order Fractionalization Hypothesis proposes an alternative class of half-integer spin or odd-integer charge condensate, resulting from the spontaneous formation of symmetry-breaking bound, composite fermions. Here, the bound-state wavefunction, which carries half-integer spin or odd-integer charge acts as a bosonic condensate. Using mean-field and numerical RG techniques, we demonstrate this idea using the two-channel Kondo problem, showing that various different classes of three-body bound-state formation develop in response to different applied patterns of channel symmetry breaking. In a lattice, these various patterns of symmetry breaking feed back to drive spontaneous three-body bound-state formation, inducing a form of order that lies outside the Hartree-Fock BCS paradigm. We discuss a provisional categorization of fractionalized order and possible applications to heavy fermion and other strongly correlated materials.