Abstract
We discuss the properties of the non-Hermitian 𝒫𝒯-symmetric two–scalar fields model. We investigate stability areas of this system and properties of vortices that emerge in the system of two interacting scalar fields. The phase diagram of the model contains stable and unstable regions depending on 𝒫𝒯-symmetry breaking, which intercross the regions of U(1)-symmetric and U(1)-broken phases in a nontrivial way. At non-zero quartic couplings, the non-Hermitian model possesses classical vortex solutions in the 𝒫𝒯-symmetric regions. We also consider a close Hermitian analog of the theory and compare the results with the non-Hermitian model.
Highlights
Traditional quantum mechanics requires the Hamiltonian to be Hermitian
The Hermiticity condition can be replaced by the requirement that the Hamiltonian of the system enjoys the invariance under the combined parity P and time-reversal inversion T operation (PT -symmetry) [1, 2]: H = HPT, (1)
Our work considers the non-Hermitian model of two self-interacting complex scalar fields
Summary
Traditional quantum mechanics requires the Hamiltonian to be Hermitian. This condition guarantees that the energy spectrum is real-valued and the time evolution of the system is unitary. The Hermiticity condition can be replaced by the requirement that the Hamiltonian of the system enjoys the invariance under the combined parity P and time-reversal inversion T operation (PT -symmetry) [1, 2]: This symmetry of the Hamiltonian ensures the real-valued energy spectrum and, the unitary evolution and stability of the system unless the PT -symmetry is broken spontaneously. The topological solutions in the multicomponent scalar models appear in various systems ranging from condensed matter to high energy physics. Some of these models can serve as viable extensions of the Standard Model of fundamental particle interactions [20,21,22,23]
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