Reentrant Localization Transition in a Quasiperiodic Thue-Morse Chain

Abstract

We investigate single-particle localization in a dimerized Su--Schrieffer--Heeger (SSH) chain with a quasiperiodic onsite potential masked by the deterministic Thue--Morse sequence. Using exact diagonalization, we map the localization behavior as a function of the quasiperiodic potential strength and hopping dimerization through the correlation dimension, inverse participation ratio, and normalized participation ratio. For appropriate hopping ratios, increasing the potential strength drives the mid-spectrum states through a localized--multifractal--localized sequence, producing a reentrant recovery of participation before localization is restored at stronger modulation. Energy-resolved diagnostics show that this recovery is concentrated in the central spectral region rather than occurring uniformly throughout the spectrum. Extrapolations of the generalized dimensions to the thermodynamic limit reveal a systematic moment-dependent hierarchy in the reentrant window, accompanied by a broadened thermodynamic-limit singularity spectrum. Real- and momentum-space diagnostics provide complementary evidence for multifractal scaling in this regime, while two-size crossings yield finite-size estimates of the reentrant boundaries. Comparisons with random, globally balanced, pair-canceling, and block-permuted masks show that short-range sign anticorrelation promotes reentrance when it is aligned with the dominant SSH hopping bonds. The resulting reduction of the onsite mismatch across the strong bonds provides an effective-dimer interpretation of the reentrant response, while longer-range Thue--Morse correlations modify its location and strength.