Fragment quantum embedding using the Householder transformation: A multi-state extension based on ensembles

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Density Matrix Embedding Theory (DMET) has been reformulated using Householder transformations for fragment embedding.
• Previous work focused on ground-state calculations using a non-interacting one-electron reduced density matrix.

Purpose of the Study:

• To extend the Householder transformation-based DMET to describe multiple electronic states, including ground and excited states.
• To develop an ensemble embedding method for accurate fragment embedding.

Main Methods:

• Utilized an ensemble non-interacting density matrix as a reference.
• Applied successive Householder transformations to generate an expanded set of bath orbitals.
• Demonstrated the method in single-shot DMET calculations.

Main Results:

• Achieved exact fragment embedding for multiple electronic states.
• Proved that the number of additional bath orbitals scales with fractionally occupied natural orbitals.
• Successfully described ground and first excited states in a Hubbard model and a hydrogen system.

Conclusions:

• The ensemble embedding approach using Householder transformations is feasible for describing multiple electronic states.
• The method provides a larger set of bath orbitals, enhancing accuracy.
• Future work can focus on self-consistency to further improve ensemble embedding.