Quantum critical properties of non-Hermitian XY models with magnetic field

The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.