Volume-to-area law entanglement transition in a non-Hermitian free fermionic chain

We consider the dynamics of the non-Hermitian Su-Schrieffer-Heeger model arising as the no-click limit of a continuously monitored free fermion chain where particles and holes are measured on two sublattices. The model has PT 𝒫 𝒯 -symmetry, which we show to spontaneously break as a function of the strength of measurement backaction, resulting in a spectral transition where quasiparticles acquire a finite lifetime in patches of the Brillouin zone. We compute the entanglement entropy’s dynamics in the thermodynamic limit and demonstrate an entanglement transition between volume-law and area-law scaling, which we characterize analytically. Interestingly we show that the entanglement transition and the PT 𝒫 𝒯 -symmetry breaking do not coincide, the former occurring when the entire decay spectrum of the quasiparticle becomes gapped.