Complete-graph tensor network states : a new fermionic wave function ansatz for molecules

We present a class of tensor network states specifically designed to capture the electron correlation within a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a complete-graph tensor network (CGTN) ansatz, which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. This ansatz applied to molecules is new and based on a tensor network wave function recently studied in lattice problems. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration, in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states, which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spins for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm.