Abstract
Exactly soluble models of multi-species anyons are studied on a torus and ground-state wave functions are explicitly obtained. These models describe quasi-excitations of recently discovered fractional quantum Hall states in double-layer electron systems. The representation of the braid group on a torus by the multi-species anyons is examined, and its relationship with ground-state wave functions is clarified. The braid group on a torus requires that the anyon wave function must be multi-component. However, the gauge-covariant wave functions are single-component in the present formalism. We find that zero modes of the Chern-Simons (CS) gauge fields play an essentially important role to link the anyon wave function and the braid group on a torus. Elements of the braid group of noncontractible cycles on a torus induce a “fractional” large gauge transformation of the zero modes, and the canonical commutation relation of the CS zero modes induces the braid-group algebra on a torus. The quantum Hall state in anyon systems is also discussed by comparing the anyon wave functions with the Laughlin and Halperin states.
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