Scaling law

Quantum mechanics

Mathematical physics

Essential singularity

Entropy (arrow of time)

Gravitational singularity

Critical point (mathematics)

Singularity

Mathematical optimization

Hamiltonian (control theory)

Scaling

Physics

Quantum entanglement

Mathematics

Ising model

Political science

Unitary state

Mathematical analysis

Geometry

Quantum

Hermitian matrix

Physical review. B./Physical review. B

We show that a class of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians realizing the Yang-Lee edge singularity exhibits an entanglement transition in the long-time steady state evolved under the Hamiltonian. Such a transition is induced by a level crossing triggered by the critical point associated with the Yang-Lee singularity and hence is first-order in nature. At the transition, the entanglement entropy of the steady state jumps discontinuously from a volume-law to an area-law scaling. We exemplify this mechanism using a one-dimensional transverse field Ising model with additional imaginary fields, as well as the spin-1 Blume-Capel model and the three-state Potts model. We further make a connection to the forced-measurement induced entanglement transition in a Floquet non-unitary circuit subject to continuous measurements followed by post-selections. Our results demonstrate a new mechanism for entanglement transitions in non-Hermitian systems harboring a critical point.

Yang-Lee edge singularity triggered entanglement transition