A 'Dysonization' scheme for identifying quasi-particles using non-Hermitian quantum mechanics

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Dyson's 1956 analysis of ferromagnets used a non-Hermitian Hamiltonian for spin waves.
• Non-Hermitian quantum mechanics formalism has advanced significantly since Dyson's initial work.
• Understanding low-energy excitations in magnetic materials is crucial for technological applications.

Purpose of the Study:

• To re-examine Dyson's ferromagnet analysis using modern non-Hermitian quantum mechanics.
• To extend Dyson's framework to doped anti-ferromagnets within the t-J model.
• To explore potential insights into high-temperature superconductivity.

Main Methods:

• Recasting Dyson's Hamiltonian in terms of two distinct inner products.
• Ensuring the Hamiltonian is self-adjoint with respect to these inner products.
• Applying the extended formalism to the t-J model for anti-ferromagnets.

Main Results:

• Dyson's ferromagnet analysis is reformulated, demonstrating the Hamiltonian's self-adjoint nature under specific inner products.
• The methodology is successfully extended to doped anti-ferromagnets described by the t-J model.
• A new perspective on spin wave quasi-particles and their interactions is provided.

Conclusions:

• The study provides a rigorous reinterpretation of Dyson's work through the lens of advanced non-Hermitian quantum mechanics.
• The extension to the t-J model offers a novel theoretical framework for investigating complex magnetic systems.
• This research paves the way for deeper understanding of phenomena like high-temperature superconductivity.