Emergent U(1) gauge theory with fractionalized boson/fermion from the bose condensation of exciton in multi-band insulator

Abstract

Fractionalized phases are studied in a low energy theory of exciton bose condensate in a multi-band insulator. It is shown that U(1) gauge theory with either fractionalized boson or fermion can emerge out of a single model depending on the coupling constants. Both the statistics and spin of the fractionalized particles are dynamically determined, satisfying the spin-statistics theorem in the continuum limit. We present two mutually consistent descriptions for the fractionalization. In the first approach, it is shown that fractionalized degree of freedom emerges from reduced phase space constrained by strong interaction and that the U(1) gauge field arises as a collective excitation of the low energy modes. In the second approach, complimentary descriptions are provided for the fractionalization based on world line picture of the original excitons. The emergent gauge structure is identified from the fluctuating web of exciton world lines which, in turn, realizes the string net condensation in a space-time picture.