Tree Tensor Network State with Variable Tensor Order

Autor(en)

V. Murg, F. Verstraete, R. Schneider, P. R. Nagy, Ö. Legeza

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Eötvös Loránd University Budapest, Ghent University , Technische Universität Berlin, Budapest University of Technology and Economics, Magyar Tudományos Akadémia

Journal

Journal of Chemical Theory and Computation

Band

11

Seiten

1027-1036

Anzahl der Seiten

10

ISSN

1549-9618

DOI

https://doi.org/10.1021/ct501187j

Publikationsdatum

03-2015

Peer-reviewed

Ja

ÖFOS 2012

103024 Quantenfeldtheorie, 104017 Physikalische Chemie

Schlagwörter

ASJC Scopus Sachgebiete

Computer Science Applications, Physical and Theoretical Chemistry

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/03e63d87-7269-4d20-95e0-45c1da7f9ba4