PT phase transition in higher-dimensional quantum systems

TL;DR

This paper analytically investigates parity-time (PT) phase transitions in higher-dimensional quantum systems, specifically in anisotropic oscillators influenced by magnetic fields, revealing how symmetry and anisotropy affect PT symmetry breaking.

Contribution

It provides an analytical study of PT phase transitions in higher-dimensional quantum oscillators with anisotropy and magnetic fields, highlighting the role of symmetry and system parameters.

Findings

Unbroken PT symmetry correlates with the system’s rotational symmetry.

PT phase transition is suppressed when the 2d oscillator becomes isotropic.

Magnetic field strength influences the occurrence of PT phase transition.

Abstract

We consider a 2d anisotropic SHO with {\bf ixy} interaction and a 3d SHO in an imaginary magnetic field with $\vec\mu_l$.$\vec B$ 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.