Time-dependent density functional theory with twist-averaged boundary conditions

TL;DR

This paper extends twist-averaged boundary conditions to time-dependent density functional theory, effectively reducing finite volume artifacts in simulations of quantum systems, especially in nonlinear regimes.

Contribution

The authors introduce a time-dependent TABC method for DFT, improving the treatment of boundary artifacts in finite quantum system simulations.

Findings

TABC reduces finite volume effects significantly.

TABC and ABC are similar in linear regimes but differ in nonlinear regimes.

Method works for small and large amplitude nuclear vibrations.

Abstract

Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent framework and apply it to resolve the box artifacts for finite quantum systems using as test case small- and large-amplitude nuclear vibrations. We demonstrate that by using such a method, one can reduce finite volume effects drastically without adding any additional parameters. While they are almost equivalent in the linear regime, TABC and ABC differ in the nonlinear regime in their treatment of evaporated particles.