Quantifying fermionic decoherence in many-body systems

Area of Science:

• Quantum Chemistry
• Many-Body Physics
• Computational Chemistry

Background:

• Electronic decoherence is crucial for understanding quantum systems.
• Traditional purity measures require N-particle density matrices, which are computationally challenging for large systems.
• Reduced density matrices (RDMs) are more accessible but require new methods to quantify coherence.

Purpose of the Study:

• Introduce practical measures of electronic decoherence, termed distilled purities.
• Develop methods to quantify coherence using more accessible r-body reduced density matrices (r-RDMs).
• Analyze the quantum dynamics of many-electron systems using these new coherence measures.

Main Methods:

• Define distilled purities as derivative quantities of r-body reduced purities.
• Exploit the structure of reduced purities to extract coherences between Slater determinants.
• Derive exact expressions for one-body and two-body distilled purities.

Main Results:

• Distilled purities provide a practical platform to quantify electronic coherences in a given basis.
• The method was applied to analyze the dynamics of oligo-acetylene using the Su-Schrieffer-Heeger Hamiltonian.
• Demonstrated the utility of distilled purities for analyzing quantum dynamics.

Conclusions:

• Distilled purities offer a computationally feasible approach to assess electronic decoherence.
• These measures are valuable for studying the quantum dynamics of complex many-electron systems.
• Comparison of purity, reduced purity, and distilled purity highlights their respective advantages and limitations.