Conventional quantum phase transition driven by a complex parameter in a non-HermitianPT−symmetricIsing model

Abstract

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 the non-Hermitian $\mathcal{PT}\ensuremath{-}\mathrm{symmetric}$ Ising model, which is driven by a staggered complex transverse field. Exact solution shows that the Laplacian of the ground-state energy density, with respect to real and imaginary components of the transverse field, diverges on the boundary in the complex plane. The phase diagram indicates that the imaginary transverse field has the effect of shrinking the paramagnetic phase. In addition, we also investigate the connection between the geometric phase and the QPT.