2014/12/18 by Szilárd Szalay, Max Pfeffer, Valentin Murg +4 · 1 citation
Physics and Astronomy · Mathematics · #physics.chem-ph #cond-mat.str-el #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1002/qua.24898
published as Int. J. Quant. Chem. 115, 1342 (2015) · Tutorial-review paper, 107 pages, 44 figures, 277 references. Comments are welcome
arxiv created 2014/12/18 · arxiv updated 2015/09/02
The treatment of high-dimensional problems such as the Schrödinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods, -- developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools -- can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum chemistry" at the Workshop on Theoretical Chemistry, 18 - 21 February 2014, Mariapfarr, Austria.