Anomalous optical absorption in a random system with scale-free disorder

Optical spectroscopy usually fails in detecting localization-delocalization (Anderson) transitions. We report on an anomalous behavior of the absorption spectrum in a one-dimensional lattice with long-range correlated diagonal disorder, having a power-like spectrum S(k)similar to 1/k(alpha). This type of correlations gives rise to a phase of extended states at the band center, provided alpha is larger than a critical value alpha(c). We show that for alphaalpha(c), signaling the occurrence of the Anderson transition. The peak is located slightly below the low-energy mobility edge, providing a unique spectroscopic tool to monitor the latter. We present qualitative arguments explaining this anomaly.