Applying tensor decompositions to strongly correlated quantum systems

• Applicant: Dr. Henrik Larsson
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2018 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 413079980

Many fascinating quantum systems such as the electronic structure of bioinorganic complexes or both the electronic and vibrational structure of systems undergoing a chemical reaction exhibit strong correlation. Such systems typically need to be simulated by intricate methods that have a very steep computational scaling with respect to system size. This steep scaling is essentially caused by high-dimensional tensors, that is, large tables of data. Methods to approximate them are currently revolutionizing many scientific fields, including machine learning, condensed matter physics, electronic structure theory (EST) and molecular quantum dynamics (MQD). One particular example are matrix product states (MPS). In EST, they have become an essential tool to compute large and strongly correlated systems of biological relevance. They are less explored in MQD.A generalization of MPS are tensor network states (TNS). They overcome fundamental limitations of MPS and have proven to be very useful in condensed matter physics but have not yet been explored neither in EST nor in MQD.The aim of this project is to utilize both MPS and TNS for describing strongly correlated systems both in EST and MQD. Researchers in these areas have developed similar methods, but largely isolated from each other. A central part of this project is to trigger and to utilize cross-fertilizations of ideas between these areas.One third of the project will apply the well-established methodology from condensed matter physics and EST for MPS to grid-based MQD. Compared to state-of-the-art methods in MQD, MPS offer a simpler algorithmic structure and a lower computational scaling with respect to system size. The final task will be applications to challenging systems that are very difficult to handle with current methods, especially the computation of the vibrational structure of floppy and strongly correlated molecules.The remaining two thirds of the project will deal with developing grid-based TNS for EST. Compared to conventional approaches in EST, the proposed technique is fundamentally different and resembles more the grid-based methods extensively used in MQD. MPS of the first part of the project are the foundations of TNS. TNS have the distinctive advantage of being able to represent strongly correlated molecules and other quantum systems with a linear scaling of system size (number of grid points). Ultimately, this will enable computations of systems that are currently beyond reach with existing methods.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Garnet K. Chan