Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes

TL;DR

This paper introduces high-performance spectral-based numerical schemes, including Gaussian and basis transformed propagation, to efficiently simulate time-dependent quantum systems like carbon nanotubes, significantly reducing computational costs.

Contribution

The paper presents novel spectral propagation schemes, including BTPS, that improve computational efficiency for time-dependent quantum simulations, applied here to carbon nanotubes.

Findings

BTPS offers superior computational efficiency.

The schemes accurately simulate AC response of carbon nanotubes.

Reduction in simulation times compared to traditional methods.

Abstract

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the AC response of a (5,5) carbon nanotube within a 3D real-space mesh framework.