Center for Molecular Modeling - FWO K. Gunst FWO3F02016002701

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

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

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

International school on Tensor Product State Simulations of Strongly Correlated Systems

wim — Wed, 26 Oct 2016 12:50:05 +0000

Dresden, Germany

Tuesday, 1 November, 2016 to Saturday, 5 November, 2016

Participant(s)

K. Gunst

Project ref.

FWO K. Gunst FWO3F02016002701

Conference reference

TENSOR 16

K. Gunst

wim — Wed, 19 Oct 2016 11:31:10 +0000

Project promotor

D. Van Neck

Financierende instantie

FWO-aspirant

Project data

01/10/2016 to 30/09/2020

Mandaatmaanden

Project titel

Personeel

K. Gunst

Project ref.

FWO K. Gunst FWO3F02016002701

Modern Wavefunction Methods in Electronic Structure Theory

wim — Tue, 04 Oct 2016 06:41:49 +0000

Mainz, Germany

Monday, 3 October, 2016 to Saturday, 8 October, 2016

Participant(s)

K. Gunst, C. Lanssens

Project ref.

FWO K. Gunst FWO3F02016002701

Conference reference

Modern Wavefunction Methods in Electronic Structure Theory