Apoptosis of moving, non-orthogonal basis functions in many-particle quantum dynamics

TL;DR

This paper introduces a method for selectively removing basis functions in many-particle quantum dynamics to improve numerical stability and convergence, demonstrated on spin-boson and polaron models.

Contribution

It proposes a novel approach of 'apoptosis' of basis functions, opposite to spawning, to enhance convergence in non-orthogonal basis quantum simulations.

Findings

Improved numerical stability in quantum dynamics simulations.

Effective application to spin-boson and polaron models.

Demonstrated convergence with fewer basis functions.

Abstract

Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis functions is routinely applied. Here we advocate the opposite process: the programmed removal of motional freedom of selected basis functions. This is a necessity for converged numerical results with respect to the size of a non-orthogonal basis, because generically two or more states approach each other too closely early on, rendering unstable the matrix inversion, required to make the equations of motion explicit. Applications to the sub-Ohmic spin-boson model as well as to polaron dynamics in a Holstein molecular crystal model demonstrate the power of the proposed methodology.