Center for Molecular Modeling - F. Verstraete

Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry

kgunst — Wed, 21 Aug 2019 18:03:29 +0000

K. Gunst, F. Verstraete, D. Van Neck

Journal of Chemical Theory and Computation (JCTC)

15, 2996-3007

2019

Abstract

We extend the three-legged tree tensor network state (T3NS) [J. Chem. Theory Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group symmetries. T3NS intersperses physical tensors with branching tensors. Physical tensors have one physical index and at most two virtual indices. Branching tensors have up to three virtual indices and no physical index. In this way, T3NS combines the low computational cost of matrix product states and their simplicity for implementing symmetries, with the better entanglement representation of tree tensor networks. By including spin and point group symmetries, more accurate calculations can be obtained with lower computational effort. We illustrate this by presenting calculations on the bis($\mu$-oxo) and $\mu-\eta^2:\eta^2$ peroxo isomers of $[\mathrm{Cu}_2\mathrm{O}_2]^{2+}$. The used implementation is available on github.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1021/acs.jctc.9b00071

Private attachment

acs.jctc_.9b00071.pdf

T3NS: Three-Legged Tree Tensor Network States

kgunst — Thu, 15 Mar 2018 09:07:08 +0000

K. Gunst, F. Verstraete, S. Wouters, Ö. Legeza, D. Van Neck

Journal of Chemical Theory and Computation

14 (4), pp 2026–2033

2018

Abstract

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N$_2$, and the bis(μ-oxo) and μ–η$^2$:η$^2$ peroxo isomers of [Cu$_2$O$_2$]$^{2+}$.

DOI

http://dx.doi.org/10.1021/acs.jctc.8b00098

A combined density functional theory and tensor network approach to simulate strongly correlated quasi-one-dimensional materials

mieke — Mon, 04 Aug 2025 10:26:08 +0000

Q. Staelens

Master of Science in Physics and Astronomy

2025

Supervisors

Prof. Dr. ir. Veronique Van Speybroeck, prof. dr. ir. Frank Verstraete

Investigating electron correlation effects via advanced many-body techniques to describe the photovoltaic properties of complex perovskites

mieke — Mon, 04 Aug 2025 10:22:23 +0000

M. De Bosscher

Master of Science in Physics and Astronomy

2025

Supervisors

Prof. Dr. ir. Veronique Van Speybroeck, prof. dr. ir. Frank Verstraete

Increasing the accuracy of quantum-mechanical simulations for strongly correlated functional materials by designing effective Hamiltonians

leen — Thu, 06 Feb 2025 13:04:02 +0000

D. Verraes

Master of Science in Engineering Physics

2023

Supervisors

Prof. Dr. ir. Veronique Van Speybroeck; Prof. Frank Verstraete

The mystery of high-temperature superconductivity: solving effective Hamiltonians of cuprates with tensor networks

leen — Thu, 06 Feb 2025 12:55:09 +0000

S. De Meyer

Master of Science in Engineering Physics

2023

Supervisors

Prof. Frank Verstraete; Prof. Dr. ir. Veronique Van Speybroeck

Implementing downfolding algorithms to perform quantum-mechanical simulations for strongly correlated functional materials

leen — Tue, 04 Feb 2025 13:54:16 +0000

S. Ganne

Master of Science in Engineering Physics

2024

Supervisors

Prof. Dr. ir. Veronique Van Speybroeck, Prof. Frank Verstraete

Simulating the entanglement dynamics in metal-organic frameworks: a marriage between density functional theory and tensor networks

leen — Mon, 21 Mar 2022 09:21:24 +0000

The mystery of high-temperature superconductivity: ab-initio calculations using density-functional theory, downfolding and tensor networks

leen — Mon, 21 Mar 2022 08:53:35 +0000

Investigating electron correlation effects via advanced many-body techniques to describe the photovoltaic properties of complex perovskites

leen — Thu, 17 Mar 2022 13:33:06 +0000