The Wannier-Stark ladder (WSL) dynamically alters the entanglement behavior of non-Hermitian free fermions. Using the single-particle correlation matrix, we studied the effective Hamiltonian of these fermions with WSL. By examining the half-chain entanglement entropy (EE) under open boundary conditions (OBCs), we identified two different area law regions and an algebraic scaling region. Finite-size scaling revealed the critical scaling behavior of the half-chain EE. This system also shows distinct entanglement behavior under periodic boundary conditions (PBCs), differing from (1+1)D conformal field theory (CFT) under Anderson localizations scenarios. Our work paves the way for exploring the intriguing entanglement phases arising from the interplay between the non-Hermitian Skin effect (NHSE) and Wannier-Stark localization.
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Li et al. (2024) studied this question.
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