Volume-to-area law entanglement transition in a non-Hermitian free fermionic chain
Youenn Le Gal, Xhek Turkeshi, Marco Schirò
Abstract
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 \mathcal{PT} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mrow> </mml:math> -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 \mathcal{PT} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mrow> </mml:math> -symmetry breaking do not coincide, the former occurring when the entire decay spectrum of the quasiparticle becomes gapped.