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Advances in Mathematical Physics
Volume 2018 (2018), Article ID 3732892, 6 pages
Research Article

Exact Formulation of the Transverse Dynamic Spin Susceptibility as an Initial-Value Problem

Department Physik, Universität Paderborn, 33095 Paderborn, Germany

Correspondence should be addressed to Arno Schindlmayr

Received 18 August 2017; Accepted 13 December 2017; Published 3 January 2018

Academic Editor: John D. Clayton

Copyright © 2018 Arno Schindlmayr. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The transverse dynamic spin susceptibility is a correlation function that yields exact information about spin excitations in systems with a collinear magnetic ground state, including collective spin-wave modes. In an ab initio context, it may be calculated within many-body perturbation theory or time-dependent density-functional theory, but the quantitative accuracy is currently limited by the available functionals for exchange and correlation in dynamically evolving systems. To circumvent this limitation, the spin susceptibility is here alternatively formulated as the solution of an initial-value problem. In this way, the challenge of accurately describing exchange and correlation in many-electron systems is shifted to the stationary initial state, which is much better understood. The proposed scheme further requires the choice of an auxiliary basis set, which determines the speed of convergence but always allows systematic convergence in practical implementations.