Calculating the linear response functions of non-interacting electrons by the time-dependent Schroedinger equation

TL;DR

This paper introduces an efficient O(N) algorithm for computing linear response functions of non-interacting electrons by numerically solving the time-dependent Schrödinger equation, enabling large-scale simulations without extensive storage.

Contribution

The paper presents a novel O(N) algorithm that avoids matrix diagonalization, allowing for efficient calculation of response functions in large electron systems.

Findings

Achieves O(N) computational complexity for response functions

Handles systems with thousands of atoms efficiently

Does not require large storage of state vectors

Abstract

An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and suitable to parallel- and vector- computation. Since it avoids O(N^3) computational effort of matrix diagonalization, it requires only O(N) computational effort where N is the dimension of the statevector. This O(N) algorithm is very effective for systems consisting of thousands of atoms, since otherwise we have to calculate large number of eigenstates, i.e., the occupied one-electron states up to the Fermi energy and the unoccupied states with higher energy. The advantage of this method compared to the Chebyshev polynomial method recently developed by Wang (L.W. Wang, Phys. Rev. B49, 10154 (1994);L.W. Wang, Phys. Rev. Lett. 73, 1039 (1994)) is that our method can calculate linear response functions without any storage of huge statevectors on external storage. Therefore it can treat much larger systems.