Susceptibility formulation of density matrix perturbation theory.

Area of Science:

• Quantum Chemistry
• Materials Science
• Computational Physics

Background:

• Density matrix perturbation theory offers efficient time-independent response calculations.
• Linear response is typically derived from Hamiltonian perturbations.
• Existing methods can be computationally intensive for large systems.

Purpose of the Study:

• To present a dual formulation for calculating static susceptibility.
• To enable efficient linear response calculations for various Hamiltonian perturbations.
• To integrate quantum response calculations with AI hardware.

Main Methods:

• Recursive Fermi-operator expansions for density matrix perturbation theory.
• Dual formulation calculating static susceptibility of an observable.
• Generalizations for fractional occupation numbers and self-consistent linear response.
• Integration with sparse matrix algebra and deep neural networks (AI).

Main Results:

• The dual susceptibility formulation provides an alternative to traditional density matrix perturbation theory.
• This approach maintains computational efficiency and linear scaling complexity for sparse systems.
• Demonstrated performance of recursive susceptibility calculations using NVIDIA GPUs and Tensor Cores.

Conclusions:

• The dual susceptibility formulation is a computationally efficient framework for quantum response calculations.
• Integration with AI hardware offers new possibilities for leveraging advanced computing resources.
• This method advances the study of quantum chemistry and materials science response properties.