Fingerprints of Loop Quantum Gravity Black Holes with Quintessence Field

In this study, we investigate a static, spherically symmetric black hole (BH) within the framework of Loop Quantum Gravity (LQG) surrounded by quintessence field. Our comprehensive analysis shows that the interplay between quantum corrections and exotic matter produces unique spacetime features, most notably a triple-horizon structure for specific parameter combinations. We derive the metric function incorporating both LQG parameters ($\alpha$, $B$) and quintessence parameters ($c$, $w$), analyzing its implications for horizon structure through embedding diagrams. We examine null and timelike geodesics, calculating photon spheres, effective potentials, and orbital dynamics. Our study demonstrates how quantum and quintessence parameters affect BH shadow size and shape, offering potential observational signatures. Through scalar perturbation analysis, we compute quasinormal modes (QNMs) frequencies, confirming the stability of these hybrid BHs while identifying distinctive spectral characteristics. Finally, using the Gauss-Bonnet (GB) theorem modified approach, we derive an analytical expression for gravitational deflection angles, showing a hierarchical structure of contributions from classical, quintessence, and quantum effects at different distance scales.