Entanglement phase transitions in non-Hermitian quasicrystals

The scaling law of entanglement entropy could undergo qualitative changes during the nonunitary evolution of a quantum many -body system. In this work, we uncover such entanglement phase transitions for free fermions in one-dimensional non -Hermitian quasicrystals (NHQCs). We identify two types of entanglement transitions with different scaling laws and critical behaviors due to the interplay between non -Hermitian effects and quasiperiodic potentials. The first type represents a typical volume -law to area -law transition, which happens together with a PT -symmetry breaking and a localization transition. The second type features an abnormal log -law to area -law transition, which is mediated by a critical phase with a volume -law scaling in the steady-state entanglement entropy. These entangling phases and transitions are demonstrated in two representative models of noninteracting NHQCs. Our results thus advance the study of entanglement transitions in non -Hermitian disordered systems and further disclose the rich entanglement patterns in NHQCs.