Reentrant localization length in a quasiperiodic thue-morse chain

We investigate single-particle localization in a dimerized Su–Schrieffer–Heeger chain whose quasiperiodic onsite potential is masked by the deterministic Thue–Morse sequence. The behavior is characterized by the transfer-matrix Lyapunov exponent, and by the participation moments of exactly diagonalized chains. For intracell-dominated hopping the mid-spectrum Lyapunov exponent depends nonmonotonically on the potential strength, developing a pronounced minimum that enhances the localization length by an order of magnitude over an intermediate window, whereas an intercell-dominated chain responds monotonically. The exponent remains positive at every sampled nonzero potential strength and at every state of the spectral sector, and the second participation moment saturates over the full range of system sizes, so the intermediate window is an enhancement of a finite localization length and not a change of localization class. Finite-size generalized dimensions follow the same response in real space and in the Fourier-conjugate representation, while their moment-order separation decreases systematically with size. Controlled sign masks identify the origin: the response requires short-range sign anticorrelation aligned with the dominant bonds, and displacing the modulation by a single site, which destroys the exactness of that anticorrelation while leaving the sequence otherwise intact, removes the response entirely. An effective-dimer description relates the alignment to the division of the onsite modulation between the internal detuning of a bonded pair and its common-mode energy.