Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only...

Area of Science:

• Quantum mechanics
• Computational chemistry
• Condensed matter physics

Background:

• The complexity of many-electron Hamiltonians often limits computational approaches.
• Isomorphisms between different Hamiltonian representations can offer new solution pathways.

Purpose of the Study:

• To establish and explore the isomorphism between multi-state and second-quantized many-electron Hamiltonians.
• To demonstrate the transferability of solution methods between these Hamiltonian types.

Main Methods:

• Establishing a mathematical isomorphism between the Hamiltonians.
• Utilizing the resonant level (Landauer) model for nonequilibrium quantum transport as a test case.
• Applying previously developed classical mapping models for multi-state Hamiltonians.

Main Results:

• The isomorphism holds, enabling method transfer.
• Classical mapping models yield exact results for the resonant level model.
• The approach is extendable to Hamiltonians with two-electron interactions.

Conclusions:

• The established isomorphism provides a powerful tool for quantum many-body problems.
• This work bridges methodologies in quantum transport and electronic structure theory.
• The findings offer a path to more efficient and exact calculations for complex systems.