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Abstract

We study many-body localization (MBL) in a spin-chain model mimicking the Rydberg-blockade quantum simulator with infinite-strength projection and moderate quasiperiodic modulation. Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. Intriguingly, the constrained MBL transition may embody a discontinuous eigenstate phase transition, whose discontinuity nature significantly suppresses finite-size drifts that plague most numerical studies of conventional MBL transition. Through quantum dynamics, we find that rotating the modulated field from parallel toward perpendicular to the projection axis induces an eigenstate transition between diagonal and constrained MBL phases. The entanglement-entropy growth in constrained MBL follows a double-log form, whereas it changes to a power law in approaching the diagonal limit. By unveiling confined nonlocal effects in integrals of motion of constrained MBL, we show this insulating state is not a many-body Anderson insulator. Our predictions are testable in Rydberg experiments.