Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems

We study quantum phase transitions in non-Hermitian XY and transverse-field Ising spin chains, in which the non-Hermiticity arises from the imaginary magnetic field. Analytical and numerical results show that at exceptional points, coalescing eigenstates in these models close to W, distant Bell and GHZ states, which can be steady states in dynamical preparation scheme proposed by T. D. Lee et. al. (Phys. Rev. Lett. 113, 250401 (2014)). Selecting proper initial states, numerical simulations demonstrate the time evolution process to the target states with high fidelity.