Susceptibility Formulation of Density Matrix Perturbation Theory

• Main Authors: Niklasson, Anders M. N, Habib, Adela, Finkelstein, Joshua, Rubensson, Emanuel H
• Format: Journal Article
• Language: English
• Published: 25-09-2024
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2409.17033

Density matrix perturbation theory based on recursive Fermi-operator
expansions provides a computationally efficient framework for time-independent
response calculations in quantum chemistry and materials science. From a
perturbation in the Hamiltonian we can calculate the first-order perturbation
in the density matrix, which then gives us the linear response in the
expectation values for some chosen set of observables. Here we present an
alternative, {\it dual} formulation, where we instead calculate the static
susceptibility of an observable, which then gives us the linear response in the
expectation values for any number of different Hamiltonian perturbations. We
show how the calculation of the susceptibility can be performed with the same
expansion schemes used in recursive density matrix perturbation theory,
including generalizations to fractional occupation numbers and self-consistent
linear response calculations, i.e. similar to density functional perturbation
theory. As with recursive density matrix perturbation theory, the dual
susceptibility formulation is well suited for numerically thresholded sparse
matrix algebra, which has linear scaling complexity for sufficiently large
sparse systems. Similarly, the recursive computation of the susceptibility also
seamlessly integrates with the computational framework of deep neural networks
used in artificial intelligence (AI) applications. This integration enables the
calculation of quantum response properties that can leverage cutting-edge
AI-hardware, such as Nvidia Tensor cores or Google Tensor Processing Units. We
demonstrate performance for recursive susceptibility calculations using Nvidia
Graphics Processing Units and Tensor cores.