Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules

Abstract

We present a new class of tensor network states that are specifically designed to capture the electron correlation of 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. 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 spin 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.

References in corpus (20)

• The density-matrix renormalization group
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• The ALPS project release 1.3: open source software for strongly correlated systems
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• From density-matrix renormalization group to matrix product states
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Feedback-optimized parallel tempering Monte Carlo
• Solving Gapped Hamiltonians Locally
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Ground state fidelity from tensor network representations
• Variational quantum Monte Carlo simulations with tensor-network states
• Two-Dimensional Tensor Product Variational Formulation
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• QC-DMRG study of the ionic--neutral curve crossing of LiF
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo

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