Pressure-induced hole delocalization in the strongly correlated quasicubic charge-transfer perovskite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>LaBa</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml

Analysis of the thermal and baric evolution of resistance in ${\mathrm{LaBa}}_{2}{\mathrm{Fe}}_{3}{\mathrm{O}}_{8+\ensuremath{\delta}}$ enabled the construction of its pressure-temperature (P-T) phase diagram, which prominently displays a critical boundary, ${P}_{c}^{\mathrm{MIT}}(T)$, marking the transition from localized to hole-type extended states. The relatively low critical pressures $[{P}_{c}^{\mathrm{MIT}}(T)\ensuremath{\approx}3--8\phantom{\rule{0.16em}{0ex}}\text{GPa}]$ suggest that, as $P\ensuremath{\rightarrow}{P}_{c}$ in this narrow-gap, strongly correlated charge-transfer system, both the hybridization strength and the charge-transfer character are progressively enhanced, ultimately leading to the emergence of metallicity. Emphasizing the electronic nature of this transition, pressure-dependent structural analyses at room temperature reveal no associated structural phase transition at ${P}_{c}^{\mathrm{MIT}}(T)$; the system retains a (weakly tetragonally distorted) quasicubic perovskite structure with Murnaghan-type compressibility up to 30 GPa. The emergence of hole delocalization and metallic conduction, coupled with suppressed antiferromagnetism, suggests proximity to quantum criticality.