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Model wave functions constructed from (1+1)D conformal field theory (CFT)have played a vital role in studying chiral topologically ordered systems.There usually exist multiple degenerate ground states when such states areplaced on the torus. The common practice for dealing with this degeneracywithin the CFT framework is to take a full correlator on the torus, whichincludes both holomorphic and antiholomorphic sectors, and decompose it intoseveral conformal blocks. In this paper, we propose a pure chiral approach forthe torus wave function construction. By utilizing the operator formalism, thewave functions are written as chiral correlators of holormorphic fieldsrestricted to each individual topological sector. This method is not onlyconceptually much simpler, but also automatically provides us the anyoneigenbasis of the degenerate ground states (also known as the "minimallyentangled states"). As concrete examples, we construct the full set ofdegenerate ground states for SO($n$)$_1$ and SU($n$)$_1$ chiral spin liquids onthe torus, the former of which provide a complete wave function realization ofKitaev's sixteenfold way of anyon theories. We further characterize theirtopological orders by analytically computing the associated modular $S$ and $T$matrices.

Chiral conformal field theory for topological states and the anyon eigenbasis on the torus