arXiv subjects

Taylan Yildiz

Publications and source records attributed to Taylan Yildiz.

4 recordsLinked to original sources

arXiv2026

Localization Transitions in a Half-Filled Helical Aubry-Andr\'e Model

We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-Andr\'e model with an additional $N$th-neighbor hopping term of strength $J_{N}$. This long-range tunneling couples successive windings of an effective helical chain and introduces a second control parameter beyond the quasiperiodic potential strength $\Delta$. Working with noninteracting fermions (typically at half filling), we diagnose the delocalization-localization transition using extensions of the modern theory of polarization. Specifically, we compute the polarization amplitudes of the many-body Slater-determinant ground state and construct a geometric Binder cumulant from polarization amplitudes. The critical potential where the localization transition happens is extracted from the sign change (zero crossing) of the geometric Binder cumulant. We map critical potential as a function of $J_N$ and the helical range $N$, finding that stronger helical hopping generally stabilizes the extended phase (shifting critical potential upward), while the $N$-dependence can display pronounced commensurability-induced spikes. We further compare the geometric Binder cumulant with the Fermi gap, which remains near zero at small values of potential and opens in the same parameter regime where the geometric Binder cumulant departs from extended phase. Finally, to take a controlled thermodynamic limit along Fibonacci system sizes, we employ a Zeckendorf-shift construction that fixes the many-body sector consistently as system size goes to infinity.

cond-mat.dis-nn↗

arXiv2025

Reentrant Localization Transition in a Quasiperiodic Thue-Morse Chain

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.

cond-mat.dis-nn↗

arXiv2025

Localization Properties of a Disordered Helical Chain

We study the localization properties of the quasiperiodic one-dimensional helical chain with two tunneling paths: nearest-neighbor and a long-range hop that connects sites of consecutive helical turns. Using exact diagonalization, we quantify localization employing the inverse participation ratio (IPR) and the normalized participation ratio (NPR), and combine them into a single measure to create a phase map. The resulting diagrams reveal three regimes: a completely extended phase, a completely localized phase, and a mixed domain where localized and extended states coexist. In the diagrams, we investigate the behaviors of tightly and loosely wound helices and examine a special case where the number of sites per turn is a Fibonacci number. For moderate numbers of sites per helical turn, the mixed region is broad and also shifts with the long-range coupling. When the turn size is a Fibonacci number, the phase boundary becomes nearly horizontal and the mixed region fades out, effectively recovering the standard Aubry-André model behavior.

cond-mat.dis-nn↗

arXiv2025

Localization and persistent currents in a quasiperiodic disordered helical lattice

We investigate localization and persistent currents in a helical tight-binding lattice subject to two independent magnetic fluxes and a quasiperiodic on-site potential. Working with non-interacting, spinless fermions under periodic boundary conditions, we solve the model by exact diagonalization and study localization with both inverse and normalized participation ratios. We identify boundaries separating extended, mixed, and localized regimes by constructing a diagram incorporating potential strength and inter-ring coupling. In the metallic regime, persistent currents flowing around both the toroidal and poloidal directions show oscillations whose amplitude decays as disorder grows and vanishes past the localization threshold; in the localized regime, currents become flux-insensitive. We demonstrate that tuning magnetic fluxes, hopping strengths, or quasiperiodic potential amplitudes provides control over the critical disorder threshold. Our results suggest a versatile platform for disorder-and flux-controlled switching between conductive and insulating states.

cond-mat.dis-nn↗