# Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.

@article{Nakatani2013EfficientTT, title={Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.}, author={Naoki Nakatani and Garnet Kin-Lic Chan}, journal={The Journal of chemical physics}, year={2013}, volume={138 13}, pages={ 134113 } }

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… Expand

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#### References

SHOWING 1-10 OF 81 REFERENCES

Simulating strongly correlated quantum systems with tree tensor networks

- Physics
- 2010

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the… Expand

Low entanglement wavefunctions

- Mathematics
- 2012

We review a class of efficient wavefunction approximations that are based around the limit of low entanglement. These wavefunctions, which go by such names as matrix product states and tensor network… Expand

Quantum-information analysis of electronic states of different molecular structures

- Physics
- 2011

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between… Expand

Spin-adapted density matrix renormalization group algorithms for quantum chemistry.

- Physics, Medicine
- The Journal of chemical physics
- 2012

The potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems is demonstrated by demonstrating that spin- Adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Expand

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

- Physics
- 2009

This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor… Expand

Tensor operators: Constructions and applications for long-range interaction systems

- Physics
- 2010

We consider the representation of operators in terms of tensor networks and their application to the ground-state approximation and time evolution of systems with long-range interactions. We provide… Expand

Efficient simulation of infinite tree tensor network states on the Bethe lattice

- Physics
- 2012

We show that the simple update approach proposed by Jiang et al. [H. C. Jiang, Z. Y. Weng, and T. Xiang, Phys. Rev. Lett. 101, 090603 (2008)] is an efficient and accurate method for determining the… Expand

High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds.

- Chemistry, Medicine
- The Journal of chemical physics
- 2009

The authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Expand

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group

- Mathematics
- 2002

We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yield… Expand

Optimizing the density-matrix renormalization group method using quantum information entropy

- Physics
- 2003

In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density-matrix renormalization group (DMRG) method we have studied the separability… Expand