  We compute holographic entanglement entropy (EE) and the renormalized EE in
AdS solitons with gauge potential for various dimensions. The renormalized EE
is a cutoff-independent universal component of EE. Via Kaluza-Klein
compactification of $S^1$ and considering the low-energy regime, we deduce the
$(d-1)$-dimensional renormalized EE from the odd-dimensional counterpart. This
corresponds to the shrinking circle of AdS solitons, probed at large $l$. The
minimal surface transitions from disk to cylinder dominance as $l$ increases.
The quantum phase transition occurs at a critical subregion size, with
renormalized EE showing non-monotonic behavior around this size. Across
dimensions, massive modes decouple at lower energy, while degrees of freedom
with Wilson lines contribute at smaller energy scales.
