Abstract
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.
Highlights
It has been more than a decade ago that the quantum chemistry version of the density matrix renormalization group (QCDMRG) method[1,2] has been applied to study the ionic-neutral curve crossing of LiF in order to demonstrate that it provides a globally accurate description of the system even if the wave function changes dramatically transversing the avoided crossing.[3]
Our QC-DMRG program has been developed for a long time, and it includes advanced features like the dynamic block state selection (DBSS) approach,[13,39] the configuration interaction (CI)-DEAS procedure,[12] and the treatment of orbital spatial symmetries which are not implemented yet in the tree tensor network states (TTNS) code
The present paper has been devoted to the application of the quantum-chemistry tree tensor network state (QC-TTNS) method to calculate the potential energy curve in the vicinity of the ionic−covalent avoided crossing in LiF
Summary
It has been more than a decade ago that the quantum chemistry version of the density matrix renormalization group (QCDMRG) method[1,2] has been applied to study the ionic-neutral curve crossing of LiF in order to demonstrate that it provides a globally accurate description of the system even if the wave function changes dramatically transversing the avoided crossing.[3]. A reformulation of DMRG in terms of socalled matrix product states (MPS)[18−21] has shown that it is only one special case in a much more general set of methods: the so-called tensor network states (TNS),[19,22−32] which in certain cases is expected to even outperform QC-DMRG in the near future.[33,34] A special form of TNS, the tree tensor network states (TTNS) approach,[35−38] was first applied in quantum chemistry by some of us[33] to present the underlying theoretical background and scaling properties of the QC-TTNS algorithm, while an efficient extension of the two-site QC-DMRG using the tree-like topology has been applied recently to dendrimers.[34] In this latter work, a novel half-renormalization scheme has been introduced in order to reduce computational cost related to the diagonalization of the effective Hamiltonian. The TTNS approach plays a fundamental role in hierarchical tensor decompositions, recently developed for tensor product approximation,[31] see e.g. refs 29 and 30
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