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Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model

A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian PT-symmetric Ising model, which is driven by a staggered complex transverse field. Exact solution shows that the Laplacian of the groundstate energy density, with respect to real and imaginary components of the transverse field, diverges on the boundary in the complex plane. The phase diagram indicate that the imaginary transverse field has the effect of shrinking the paramagnet phase. In addition, we also investigate the connection between the geometric phase and the QPT.