Density Matrix Perturbation Theory

Abstract

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.

4 pages, 2 figures

References in corpus (3)

• Expansion algorithm for the density matrix
• Ab initio linear scaling response theory: Electric polarizability by perturbed projection
• Implicit Purification for Temperature-Dependent Density Matrices

Cited by in corpus (19)

• O(N) methods in electronic structure calculations
• Ab initio linear scaling response theory: Electric polarizability by perturbed projection
• Generalized Extended Lagrangian Born-Oppenheimer Molecular Dynamics
• Graph-based linear scaling electronic structure theory
• Next generation extended Lagrangian first principles molecular dynamics
• Spin unrestricted linear scaling electronic structure theory and its application to magnetic carbon doped BN nanotubes
• Higher Order Response in $\mathcal{O}(N)$ by Perturbed Projection
• Non-Orthogonal Density Matrix Perturbation Theory
• Phase-space interference in extensive and non-extensive quantum heat engines
• Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory
• Canonical density matrix perturbation theory
• Linear scaling computation of the Fock matrix VII. Periodic Density Functional Theory at the $\Gamma$-point
• Linear scaling calculation of band edge states and doped semiconductors
• Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics
• Efficient Parallel Linear Scaling Method to get the Response Density Matrix in All-Electron Real-Space Density-Functional Perturbation Theory
• Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning
• Notes on density matrix perturbation theory
• Hybrid kernel polynomial method
• Split representation of adaptively compressed polarizability operator