# 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…

## 112 Citations

### Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

- PhysicsJournal of chemical theory and computation
- 2015

The TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals and a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement.

### Automatic structural optimization of tree tensor networks

- Computer SciencePhysical Review Research
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A TTN algorithm is proposed that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs and can be visualized as a perfect binary tree in the optimized TTN.

### Efficient tensor network simulation of quantum many-body physics on sparse graphs

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- 2022

It is found that message-passing inference algorithms such as belief propagation can lead to efficient computation of local expectation values for a class of tensor network states defined on sparse graphs.

### Direct density matrix renormalization group approaches for strong correlation effects in quantum chemistry

- Physics
- 2017

An implementation of the single-site density matrix renormalization group (DMRG) approach for the quantum-chemical application to calculate approximate as well as exact electronic ground-state…

### Tensor Network States with Low-Rank Tensors

- Computer Science
- 2022

It is shown that choosing the tensor rank r to be on the order of the bond dimension m, iscient to obtain high-accuracy groundstate approximations and to substantially outperform standard TTNS computations.

### Tree tensor networks and entanglement spectra

- Physics
- 2013

A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A…

### Tensor Network Contractions

- PhysicsLecture Notes in Physics
- 2020

This lecture notes focuses on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems, and revisits the TN approaches from the perspective of multi-linear algebra and quantum simulation.

### Algebraic Geometry of Tree Tensor Network States

- Mathematics
- 2014

Tree tensor networks have been used to model the ground states of Hamiltonians in condensed matter physics and quantum chemistry. Exactly which quantum states can be represented by a tree tensor…

### Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

- Computer ScienceThe Journal of chemical physics
- 2016

This work describes how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation, and discusses two improvements of the abinitio D MRG sweep algorithm motivated by matrix product operators language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism.

### Tensor networks and geometry for the modelling of disordered quantum many-body systems

- Physics, Computer Science
- 2015

This work uses DMRG to study the one dimensional disordered Bose-Hubbard model at fillings N=L = 1=2, 1 and 2 and shows that the whole phase diagram for each can be successfully obtained by analysing entanglement properties alone.

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