Author(s) :
Szilárd Szalay,
Max Pfeffer
,
Gergely Barcza,
Valentin Murg,
Frank Verstraete,
Reinhold Schneider
,
Örs Legeza
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 38-2014
MSC 2000
- 15A69 Multilinear algebra, tensor products
-
81-08 Computational methods
Abstract :
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, it is a common belief that
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 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.
Keywords :
tensor networks, DMRG, entanglement, tensor product approximation, quantum infromation