No 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

We have applied the momentum space version of the Density Matrix Renormalization Group method (k-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH2, H2O, and F2 as well as the first excited state of CH2. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500-2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000-1.200.000.

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization. We also discuss the application of the configuration interaction based dynamically extended active space procedure which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures to a great extent. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal orbital ordering and carry out efficient calculations on transition metal clusters. We propose a recipe to perform DMRG calculations in a black-box fashion and we point out the connections of our work to other tensor network state approaches.