PT phase transition in higher-dimensional quantum systems

Abstract We consider a 2d anisotropic SHO with ixy interaction and a 3d SHO in an imaginary magnetic field with μ → l . B → interaction to study the PT phase transition analytically in higher dimension. Unbroken PT symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system. PT phase transition ceases to occur the moment the 2d oscillator becomes isotropic. Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes PT phase transition depending on the strength of the magnetic field and frequency of the oscillator. All these results in higher dimensions are based on exact analytical calculations.