Pure State v-Representability of Density Matrix Embedding Theory

Area of Science:

• Quantum chemistry
• Computational condensed matter physics

Background:

• Density matrix embedding theory (DMET) requires matching density matrix blocks from high-level and low-level theories.
• Practical calculations sometimes fail to achieve exact matching, leading to vanishing low-level band gaps and numerical issues.

Purpose of the Study:

• To address the challenges in DMET calculations arising from the inability to achieve exact matching of density matrix blocks.
• To develop a method that relaxes the noninteracting pure-state v-representability (NI-PS-V) condition, which is linked to the Aufbau principle.

Main Methods:

• Developed an augmented Lagrangian method to facilitate the matching of density matrix blocks.
• Relaxed the strict requirement of the Aufbau principle in constructing the low-level density matrix.

Main Results:

• The augmented Lagrangian method successfully relaxed the NI-PS-V condition.
• In challenging cases, relaxing the Aufbau principle led to exact matching of density matrix blocks.
• The proposed method demonstrated improved accuracy in the 2D Hubbard and hydrogen model systems.

Conclusions:

• The developed augmented Lagrangian method provides a robust approach to overcome limitations in DMET calculations.
• Relaxing the Aufbau principle is a viable strategy for achieving accurate density matrix block matching and improving computational results.