Tensor product methods and entanglement optimization for ab initio quantum chemistry

Szilárd Szalay; Max Pfeffer; Valentin Murg; Gergely Barcza; Frank Verstraete; Reinhold Schneider; Örs Legeza

doi:10.1002/qua.24898

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arXiv · 1412.5829

Tensor product methods and entanglement optimization for ab initio quantum chemistry

Szilárd Szalay·Max Pfeffer·Valentin Murg·Gergely Barcza·Frank Verstraete·Reinhold Schneider·Örs Legeza

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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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Szilárd Szalay, Max Pfeffer, Valentin Murg, Gergely Barcza, Frank Verstraete, Reinhold Schneider, Örs Legeza. 2014-12-18. Tensor product methods and entanglement optimization for ab initio quantum chemistry. https://doi.org/10.1002/qua.24898

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