Distinct reentrant transitions in a quasi-periodic Raman lattice

Abstract

We investigate a one-dimensional lattice with spin-orbit coupling (SOC) and a Zeeman potential containing uniform and quasiperiodic components. By tuning SOC, anomalous mobility edges emerge that separate critical from non-critical states, yielding a reentrant transition between two mixed phases, M$_1$$\to$M$_2$$\to$M$_1$, where M$_1$ (M$_2$) lacks (hosts) anomalous mobility edges. A new \emph{reentrant criticality transition}, defined as multiple entries into the critical phase, is identified. As a counterpart to reentrant delocalization/localization transitions, it completes the basic framework of reentrant phenomena across extended, localized, and critical states. The uniform Zeeman potential drives a reentrant delocalization transition, arising from the splitting of the localized region induced by the shift of mobility edges. This reveals a distinct pathway for reentrant phenomena beyond hybridization mechanisms.