Decomposition and embedding in the stochastic GW self-energy

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• The GW approximation is crucial for accurate excited state energy calculations.
• Simulating complex systems like heterostructures requires efficient computational methods.
• Understanding localized electronic states is key in materials science.

Purpose of the Study:

• To introduce novel developments in GW approximation for computing excited state energies.
• To enhance the efficiency and accuracy of calculations for localized states.
• To gain physical insights into quantum phenomena in heterogeneous systems.

Main Methods:

• Decomposition of Green's function and screened Coulomb interaction into deterministic and stochastic parts.
• Construction of a subspace self-energy to capture dynamic correlation in specific regions.
• Application to large-scale simulations of nitrogen-vacancy states in hBN and hBN-graphene heterostructures.

Main Results:

• Deterministic embedding of localized states significantly reduces statistical errors.
• Computational cost is reduced by over an order of magnitude.
• The subspace self-energy reveals interfacial coupling effects on electronic correlations and excited-state lifetimes.

Conclusions:

• The developed methodology offers a more efficient and accurate way to compute excited state energies using the GW approximation.
• The decomposition provides new physical insights into quantum phenomena, particularly in heterogeneous systems.
• This approach is essential for accurately treating impurity states and understanding interfacial effects.