Non-Hermitian quantum systems and their geometric phases

Abstract

We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic evolution of non-Hermitian quantum systems. We find that the adiabatic evolution is possible only when the eigen-energies are real. The accompanying geometric phase is found to be generally complex and associated with not only the phase of a wavefunction but also its amplitude. The condition for the real geometric phase is laid out. Our results are illustrated with two examples of non-Hermitian $\mathcal{P}\mathcal{T}$ symmetric systems, the two-dimensional non-Hermitian Dirac fermion model and bosonic Bogoliubov quasi-particles.

7 pages, no figure

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Cited by in corpus (12)

• Floquet Topological Phases of Non-Hermitian Systems
• Quantum metric and wavepackets at exceptional points in non-Hermitian systems
• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Effect of quantum jumps on non-Hermitian system
• Collective optical properties of moiré excitons
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems
• Monopoles in non-Hermitian systems
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• A mathematical formalism of non-Hermitian quantum mechanics and observable-geometric phases