  Can localization persist when interaction grows infinitely stronger than
randomness? If so, is it many-body Anderson localization? How about the
associated localization transition in the infinite-interaction limit? To tackle
these questions, we study many-body localization (MBL) in a spin-chain model
mimicking the Rydberg-blockade quantum simulator with both 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. Remarkably, the constrained MBL transition
may embody a discontinuous eigenstate phase transition, whose discontinuity
nature significantly suppresses the 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 the diagonal and
constrained MBL phases. Intriguingly, 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 the significance of confined
nonlocal effects in integrals of motion of constrained MBL, we show that this
newfound insulating state is not a many-body Anderson insulator. Our
predictions can be tested in Rydberg experiments.
