Non-Abelian Adiabatic Evolution and Shortcuts to Adiabaticity in Non-Hermitian Systems

Key Points

• This research aims to investigate non-Abelian adiabatic evolution and shortcuts in non-Hermitian systems.
• Developed a theoretical framework for non-Abelian adiabatic evolution under a pseudo-Hermitian Hamiltonian.
• Applied numerical methods to analyze the evolution of double orthogonal eigenstates.
• Expanded the adiabatic shortcut scheme for the system and validated it through numerical simulations.
• The population of non-degenerate eigenstates drastically depends on non-Hermitian parameters and initial states.
• Adiabatic evolution in degenerate subspaces exhibits characteristics similar to Hermitian systems.
• The proposed adiabatic shortcut effectively increases evolution speed while maintaining Hermitian properties in the degenerate space.