  We introduce a novel approach for computing the twist operator correlators
(TOC) in two-dimensional conformal field theories (2d CFT) and the closely
related isomonodromic tau functions. The method stems from the formal path
integral representation of the ground state reduced density matrix in 2d CFT,
and exploits properties of the associated modular Hamiltonians. For a class of
genus-zero TOC/tau functions associated with branched covers with non-abelian
monodromy group, we present: i) a determinantal representation derived from the
correlation matrix method for free fermions, and ii) a formal integral
representation derived from the universal single-interval modular Hamiltonians.
For the class of genus-zero TOC/tau functions, we also argue an approximate
factorization property, utilizing the known ground state correlation structure
of large-$c$ holographic CFT and the universality of genus-zero TOCs. We
provide explicit examples for verifying the determinantal representation and
the approximate factorization property.
