We propose a protocol of low-temperature, strain-tuned re-entrant metal-insulator transition, and crossover between strongly correlated line-graph lattices (Lieb and Kagome). Using a nonperturbative numerical approach, we demonstrate that an applied shear strain stabilizes a metallic phase cradled in between a gapped magnetic insulator and a gapless flat band transiently localized insulator, facilitating the Lieb/Kagome interconversion. Our results on transport signatures exhibit variable scaling exponents for electrical resistivity and optical conductivity, providing clear evidence of non-Fermi liquid physics. We also define a strain-dependent thermal scale to quantify the crossover between the non-Fermi liquid and bad metal phases.

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• Flat bands
• Quantum phase transitions
• Mott insulators
• Hubbard model
• Non-Fermi-liquid theory
• Path-integral Monte Carlo