Dissipation-Assisted Matrix Product Factorization of Vibronic Networks

Organic compounds are carbon-based molecules that cluster into structures that are flexible, light-interacting and their electrical conductivity lies between that of an insulator and a semiconductor. They are cheap and easily recyclable, some self-aggregate while others can be self-repaired. They can be printed onto many different surfaces for all sorts of purposes, from energy storage to light energy harvesting. This impeccable portfolio of organic materials is heavily tarnished by their reputation of having a low power performance and being easily degradable, and the advancement of these green materials in the industrial energy landscape has yet to find more durable and scalable solutions. Notwithstanding, the spectacular progress that has taken place during the last decade in the laboratories exploring organic and hybrid compounds may revolutionize both the energy and semiconductor industries at the design and foundry level that rely the more and more on the mining of rare earth materials. The links between molecules in organic aggregates are based on noncovalent forces, which makes them relatively soft and disordered. The energy range of these weak, electronic bonds is close to that of the vibrational motion of the nuclei. For example, the double and triple carbon-carbon bonds and other long-lived intramolecular vibrations have frequencies that are high enough to mingle with electronic excitations, modulating their motion quite noticeably. For this reason we call these aggregates vibronic, as a reminder of the intimate interaction between electronic and vibrational degrees of freedom. More importantly, the mixing between vibrations and electrons may even trigger or prevent some desired events, which makes them very useful as engineering materials. If we learn one day how to tune these vibronic antennae networks into efficient biosynthetic devices, who knows what kind of technologies and devices can emerge from the merging and manipulation of sound, light and electricity? It is clear that Nature hasn’t spared this opportunity. Since electrons and vibrations operate at similar time scales, approximate theories that treat vibrations as small perturbations cannot be applied. Modeling realistic dissipative effects requires the electronic states and intramolecular vibrations to interact with quantized vibrational reservoirs at finite temperatures, making simulations of spatially extended vibronic systems particularly challenging. However, the ability to perform this type of simulations is crucial to make further progress in the understanding of transfer phenomena at the microscopic level and, in particular, discerning the possible relevance of coherent effects in the dynamics of these complexes. In the present work, we introduce a method that addresses challenges of existing methods and is able to simulate efficiently composite vibronic systems of many sites with highly structured environments. The method is composed by an efficient representation of vibronic states based in tensor networks. The structured vibrational environment will be modeled after a collection of dissipative oscillators based on a recent formulation of pseudomode theories in Open Quantum Systems. The intrinsic decoherence mechanism of the dissipative oscillator solves the “explosion” of quantum correlations that is associated with the unitary dynamics of a system plus environment model and extends considerably the available system size and time duration of simulations. One of the intentions of this dissertation is to provide also some sort of construction manual for those interested in implementing a version of the DAMPF method while learning about it. Tensors products can be initially scary because of their rough notation, so I have opted for an unorthodox geometrical representation that I believe is more gullible for newcomers. This manuscript contains everything one needs to build a minimal version of the algorithm without many intricacies.