Applying tensor decompositions to strongly correlated quantum systems
Final Report Abstract
The project aimed at describing strongly correlated electronic and vibrational quantum systems by tensor network states (TNSs). An algorithm based on the density matrix renormalization group (DMRG) has been used in for accurately computing hundreds of vibrational states of acetonitrile and the Zundel ion. The DMRG has been rigorously compared with the related multilayer multi configuration time-dependent Hartree (ML-MCTDH) method. It has been found that the DMRG can be more than an order of magnitude faster than the ML-MCTDH method. Further, TNSs with linear and tree-like topologies have been rigorously compared. For acetonitrile, it was found that tree TNSs require slightly fewer tensor sizes than linear TNSs for medium accuracies. Five projects have been initiated to explore combination of TNSs with other methods for electronic structure problems. The first projects dealt with using two-dimensional TNSs on a grid for diatomic systems. Initial results are promising but further work is required in order to gain sufficient understanding of this novel method. The second project dealt with the combination of selected configuration interaction techniques with TNSs. It was found that these two methods are very difficult to combine. Simulations of certain molecular systems such as stacked benzenes would benefit from this approach but more work is required in order to make these simulations more robust. The third project dealt with using Monte Carlo algorithms in order to optimize TNSs. The optimization turned out to be extremely difficult. The fourth project was about exploring the ”low-accuracy“ limit of linear TNSs. There, the tensors have minimal size and wavefunction symmetries are handled via a variational projector ansatz. It could be shown that this ansatz extends well-known methods such as the antisymmetrized geminal product method and the generalized valence bond method. Applications on strongly correlated benchmark systems showed promising results and an improved qualitative description of potential energy surfaces across the whole configuration space. The fourth project dealt with approximating the multireference configuration interaction (MR-CI) method by TNSs. Several methods based on the MR-CI ansatz were implemented via TNSs. Promising results on the chromium dimer, a prototypical strongly correlated electronic system, could be obtained. Simulations included MR-CI calculations with up to triple excitations into the virtual orbital space and complete active spaces with 30 electrons and 30 orbitals.
Publications
- Computing vibrational eigenstates with tree tensor network states (TTNS), J. Chem. Phys. 151, 204102 (2019)
Henrik R. Larsson
(See online at https://doi.org/10.1063/1.5130390) - Minimal Matrix Product States and Generalizations of Mean-Field and Geminal Wave Functions, J. Chem. Theory Comput. 16, 5057–5066 (2020)
Henrik R. Larsson, Carlos A. Jiménez-Hoyos, Garnet Kin-Lic Chan
(See online at https://doi.org/10.1021/acs.jctc.0c00463)
