  Recent advancements in moir\'e engineering motivate study of the behavior of
strongly-correlated electrons subject to substantial orbital magnetic flux. We
investigate the triangular lattice Hofstadter-Hubbard model at one-quarter flux
quantum per plaquette and a density of one electron per site, where geometric
frustration has been argued to stabilize a chiral spin liquid phase
intermediate between the weak-coupling integer quantum Hall and strong-coupling
120deg antiferromagnetic phases. In this work, we use Density Matrix
Renormalization Group methods and analytical arguments to analyze the
compactification of the Hofstadter-Hubbard model to cylinders of finite radius.
We introduce a glide particle-hole symmetry operation which for
odd-circumference cylinders, we show, is spontaneously broken at the quantum
Hall to spin liquid transition. We further demonstrate that the transition is
associated with a diverging correlation length of a charge-neutral operator.
For even-circumference cylinders the transition is associated with a dramatic
quantitative enhancement in the correlation length upon threading external
magnetic flux. Altogether, we argue that the 2+1D CSL-IQH transition is in fact
continuous and features critical correlations of the charge density and other
spin rotationally-invariant observables.
