Center for Molecular Modeling - K. Gunst

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

Method for making 2-electron response reduced density matrices approximately N-representable

caitlin — Thu, 01 Mar 2018 08:49:44 +0000

C. Lanssens, Paul W. Ayers, D. Van Neck, S. De Baerdemacker, K. Gunst, P. Bultinck

Journal of Chemical Physics

148, 8, 084104

2018

Abstract

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e., it has the right symmetry and normalization and it fulfills the $P$-, $Q$-, and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-$N$-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$-matrix, and $G$-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-$N$-representable 2-RDMs which are close to being $N$-representable. Through the $N$-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important $N$-representability conditions.

DOI

https://doi.org/10.1063/1.4994618

Block product density matrix embedding theory for strongly correlated spin systems

wim — Wed, 21 Jun 2017 07:14:36 +0000

K. Gunst, S. Wouters, S. De Baerdemacker, D. Van Neck

Physical Review B

95, 195127

2017

Abstract

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic J1−J2 model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.

Open Access version available at UGent repository

Green Open Access

DOI

https://doi.org/10.1103/PhysRevB.95.195127

Private attachment

CDMET.pdf

Tree tensor networks in quantum chemistry

samuel — Thu, 01 Oct 2020 07:42:00 +0000

K. Gunst

Mon, 28/09/2020

Campus Sterre S9 Krijgslaan 281, 9000 Gent

https://biblio.ugent.be/publication/8676260

Supervisors

D. Van Neck, F. Verstraete

Attachment (private)

Thesis_Klaas.pdf

Beyond Tree Tensor Networks in quantum many-body physics

samuel — Tue, 14 Jan 2020 15:31:19 +0000

J. Van Bever

Master of Science in Physics and Astronomy

2019

Supervisors

Prof. Dr. Dimitri Van Neck, Prof. Dr. ir. Toon Verstraelen

The development and adaptation of post-DMRG methods for T3NS

wim — Tue, 05 Mar 2019 10:07:31 +0000

Numerical Methods in Strongly Correlated Quantum Systems

kgunst — Wed, 07 Mar 2018 08:48:34 +0000

Marburg, Germany

Monday, 19 February, 2018 to Friday, 23 February, 2018

Participant(s)

K. Gunst

Project ref.

FWO K. Gunst FWO3F02016002701

Tree tensor networks in ab initio quantum chemistry

kgunst — Wed, 07 Mar 2018 08:41:19 +0000

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

ISBN/ISSN:

Poster

Conference / event / venue

Numerical Methods in Strongly Correlated Quantum Systems

Marburg, Germany

Monday, 19 February, 2018 to Friday, 23 February, 2018

Dispersion models with an explicit treatment of monopolar density fluctuations

wim — Mon, 05 Mar 2018 08:16:38 +0000