Real-frequency tensor trains for electronic systems

Suppose you wanted to form a model of everything and anything in the universe from the grand collisions of galaxy clusters to the subtle dance of subatomic particles how would you go about it? You might first split your problem into different parts and different scales. For example, you may justifiably ignore the relation between your last run and the movement of the tectonic plates: first, your weight dwarfs compared to the weight of the Earths crust; second, the tectonic plates move on the scale of millions of years while you move on the scale of hours, so the specifics of your run do not matter, only the total transfer of energy. That simple trick helps us break down systems: we can replace the effect of each human on tectonic movement with the sum of all of civilization that ever existed. Conversely, on the scale of a human run, we may very well think of the tectonic plates as frozen in space. The relationship of runners between each other, say, a crowd in a city marathon, on the other hand, is more difficult to figure out. Any material is also such a complicated system, and physicists and chemists have tried the same strategy of splitting the material into scales. Your chair, for example, consists of a few trillion trillion atoms, each consisting of a nucleus and electrons. The nuclei are to the electrons much like the tectonic plates are to a human they are much heavier and slower, and so to the electrons the cores appear frozen in space, whereas only the aggregate effect of the electrons matters to the cores. So we can split the material into one scale for the cores and one scale for the electrons. But heres the rub: that still leaves us with trillions of trillions of electrons, and for some materials it has proved extremely difficult for us to find additional scales, much like a crowd of runners. So here is the question: can a computer help us to discover different time scales for the electrons in a material, and also figure out how they are related? One potential method for doing just that shows extreme promise: it is called quantics tensor trains and unites ideas from machine learning and statistical physics. In this project, we hope to develop this method into a tool for understanding materials that we couldnt explain before. This project is a joint AustriaJapanese undertaking and is funded by the two funding agencies for basic research in the respective countries (FWF in Austria and JSPS in Japan). The Austrian team is led by Markus Wallerberger and Anna Kauch at the TU Wien, the Japanese team is led by Hiroshi Shinaoka at Saitama University. The FWF provides around 420,000 in funding, which mainly pays for two additional researchers over the course of three years, while the JSPS provides money for travelling and common workshops.