Welles Morgado | Searcharxiv

arXiv2026

Enhanced Multifractality Induced by Non-Hermitian Disorder in Quantum Percolation

We investigate the interplay between geometric dilution and non-Hermitian disorder in the two-dimensional quantum site-percolation model. Non-Hermiticity is introduced through random imaginary on-site potentials, representing spatially uncorrelated gain and loss, while the hopping amplitudes remain reciprocal. By combining complex level-spacing statistics, participation entropy, and multifractal analysis, we characterize the localization properties of the eigenstates as functions of the disorder and the non-Hermiticity strength. Our finite-size scaling results show that non-Hermitian disorder shifts the quantum percolation threshold ($p_q$) toward larger occupation probabilities. Consequently, the fully delocalized phase is progressively suppressed and disappears at sufficiently strong disorder. This suppression is not a simple consequence of adding on-site disorder of a given strength, but is specifically enhanced by its imaginary character, as an equally strong real (Hermitian) on-site potential produces a weaker shift of $p_q$. Nevertheless, the intermediate region between the classical ($p_c$) and quantum percolation thresholds presents a genuine multifractal critical phase, while the localization-length exponent $\nu$ remains the same, relative to its Hermitian value. Altogether, our results demonstrate that random gain and loss enhance the multifractal regime while preserving the universality class of the quantum percolation transition.

cond-mat.dis-nn↗

arXiv2026

Quantum percolation in honeycomb lattices under random spin-orbit coupling

We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold $p_q$, and the correlation-length exponent, $\nu$. In the absence of spin-orbit coupling, we find that $p_q$ remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold $p_c$ of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, $p_q$ tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.

cond-mat.dis-nn↗