Power-Law Quasiperiodic Criticality in a Non-Hermitian Ising Chain

We study a non-Hermitian Ising chain with a power-law quasiperiodic field h_j = h cos^p(2παj + φ), where the positive integer p controls the power of the modulation. The model admits an exact site-factorized similarity transformation that maps the quasi-Hermitian regime onto a real quasiperiodic Ising chain. We derive the exact zero-mode edge-localization boundary and show that the critical field on the quasi-Hermitian branch scales as 2^p, while the associated localization-length exponent remains unity for all p. At the boundary, the variance of the logarithmic coupling fluctuations is enhanced exactly by a factor of p². In the quasi-Hermitian regime, the factorized similarity transformation shows that the spatial biorthogonal entanglement spectrum is identical to that of the Hermitian counterpart. The half-chain entanglement entropy exhibits approximately logarithmic growth over the accessible sizes, with a p-dependent finite-size slope. We finally discuss a possible realization using state-selective loss and conditional no-jump dynamics.