  In the presence of strong electronic interactions, a partially filled Chern
band may stabilize a fractional Chern insulator (FCI) state, the zero-field
analog of the fractional quantum Hall phase. While FCIs have long been
hypothesized, feasible solid-state realizations only recently emerged, largely
due to the rise of moir\'e materials. In these systems, the quantum geometry of
the electronic bands plays a critical role in stabilizing the FCI in the
presence of competing correlated phases. In the limit of ``ideal'' quantum
geometry, where the quantum geometry is identical to that of Landau levels,
this role is well understood. However, in more realistic scenarios only empiric
numerical evidence exists, accentuating the need for a clear understanding of
the mechanism by which the FCI deteriorates moving further away from these
ideal conditions. We introduce and analyze an anisotropic model of a $\left|C
\right|=1$ Chern insulator, whereupon partial filling of its bands, an FCI
phase is stabilized over a certain parameter regime. We incorporate strong
electronic interaction analytically by employing a coupled-wires approach,
studying the FCI stability and its relation to the the quantum metric. We
identify an unusual anti-FCI phase benefiting from non-ideal geometry,
generically subdominant to the FCI. However, its presence hinders the formation
of FCI in favor of other competitive phases at fractional fillings, such as the
charge density wave. Though quite peculiar, this anti-FCI phase may have
already been observed in experiments at high magnetic fields. This establish a
direct link between quantum geometry and FCI stability in a tractable model far
from any ideal band conditions, and illuminates a unique mechanism of FCI
deterioration.
