Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
Abstract
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a onedimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of halfrenormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and πconjugated dendrimers) as well as nontree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In nontree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
 Publication:

Journal of Chemical Physics
 Pub Date:
 April 2013
 DOI:
 10.1063/1.4798639
 arXiv:
 arXiv:1302.2298
 Bibcode:
 2013JChPh.138m4113N
 Keywords:

 quantum chemistry;
 renormalisation;
 trees (mathematics);
 31.15.p;
 02.20.Uw;
 02.10.Ox;
 Calculations and mathematical techniques in atomic and molecular physics;
 Quantum groups;
 Combinatorics;
 graph theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 15 pages, 19 figures