Density Matrix Perturbation Theory

TL;DR

This paper introduces a quadratic convergence method for perturbing the zero temperature density matrix, enabling efficient computation of responses and energy expressions with linear scaling in the perturbed region.

Contribution

It presents a novel expansion technique that achieves quadratic convergence and linear scaling for density matrix perturbations at zero temperature.

Findings

Quadratically convergent recursive scheme for density matrix response.

Linear scaling with the size of the perturbed subsystem.

Direct computation of response functions to any order.

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.