Method for the Direct Solve of the Many-Body Schr\"{o}dinger Wave Equation

We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schr\"{o}dinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations [arXiv:1405.5073; Jerke, JCP 2015 143]; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. [SIAM 2005 26(6)] which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology.