Tensor product methods and entanglement optimization for ab initio quantum chemistry

Szalay, Szilárd and Pfeffer, M. and Murg, V. and Barcza, Gergely and Verstraete, F. and Legeza, Örs (2015) Tensor product methods and entanglement optimization for ab initio quantum chemistry. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 115 (19). pp. 1342-1391. ISSN 0020-7608

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Abstract

The treatment of high-dimensional problems such as the Schr¨odinger 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.

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