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 one-dimensional 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 half-renormalization 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 π-conjugated dendrimers) as well as non-tree 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 non-tree 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 ilustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

15 pages, 19 figures

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• 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
• From density-matrix renormalization group to matrix product states
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Finite automata for caching in matrix product algorithms
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Tensor operators: constructions and applications for long-range interaction systems
• Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance

Cited by in corpus (3)

• The density matrix renormalization group for ab initio quantum chemistry
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Tensor Networks for Lattice Gauge Theories with continuous groups