Non-Bloch parity-time-symmetric phase transition in quantum walks

Parity-time ($\mathcal{P}\mathcal{T}$) symmetry is extensively studied within non-Hermitian physical systems as it has the capability to ensure the presence of real eigenenergies of the systems characterized by non-Hermitian Hamiltonians. Previous studies have been mostly based on the Bloch band theory. Recent developments have unveiled intriguing phenomena which can only be explained by non-Bloch band theory. In this paper, we observe the $\mathcal{P}\mathcal{T}$ phase transition in photonic quantum walks, which can only be explained by the non-Bloch band theory, which relies on the open boundary condition. Furthermore, we explore the impact of disorder on $\mathcal{P}\mathcal{T}$ symmetry and demonstrate disorder-induced $\mathcal{P}\mathcal{T}$ phase transitions. Our work provides a valuable perspective for further explorations on non-Hermitian physics.