Exploring Novel Quantum Embedding Methods with Nonorthogonal Decomposition of Slater Determinants

Area of Science:

• Quantum Many-Body Physics
• Computational Chemistry
• Quantum Information Theory

Background:

• The Schmidt decomposition is fundamental to quantum many-body techniques, relying on orthogonal local basis functions.
• Existing embedding methods, such as Density Matrix Embedding Theory (DMET), utilize the Schmidt decomposition for partitioning quantum systems.
• Current methods face limitations with overlapping orbital systems and require computationally intensive mean-field calculations.

Purpose of the Study:

• To propose a generalized nonorthogonal decomposition of Slater determinants, extending the conventional Schmidt decomposition.
• To develop a flexible and efficient quantum embedding strategy for systems with overlapping orbitals.
• To bridge the gap between ab initio model potential (AIMP) embedding and DMET, improving computational efficiency and entanglement capture.

Main Methods:

• A novel nonorthogonal decomposition of Slater determinants is introduced.
• The proposed decomposition is shown to reduce to the Schmidt decomposition in the orthogonal limit.
• A new quantum embedding strategy is developed, integrating aspects of AIMP and DMET.

Main Results:

• The nonorthogonal decomposition naturally facilitates the construction of local correlation spaces for overlapping orbitals.
• This approach extends the applicability of Schmidt decomposition-based methods, like DMET, to more complex system partitions.
• The new embedding strategy bypasses the need for a full system mean-field calculation while retaining the ability to capture quantum entanglement.

Conclusions:

• The proposed nonorthogonal decomposition offers a more flexible and efficient tool for quantum many-body calculations.
• This work enhances quantum embedding methods, enabling accurate treatment of complex systems with overlapping orbitals.
• The developed strategy provides a computationally advantageous alternative for capturing quantum entanglement in many-body systems.