Center for Molecular Modeling - FWO G022914N (DVN/PB/SDB) FWOOPR2014002001

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

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CDMET.pdf

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach

wim — Thu, 12 Jan 2017 09:31:48 +0000

O.B. Ona, O. De Clercq, D.R. Alcoba, A. Torre, L. Lain, D. Van Neck, P. Bultinck

ChemPhysChem

17 (18), 2881–2889

2016

Abstract

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.

DOI

http://dx.doi.org/10.1002/cphc.201600433

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O-a_et_al-2016-ChemPhysChem.pdf

Block-ZXZ synthesis of an arbitrary quantum circuit

wim — Wed, 16 Nov 2016 14:55:23 +0000

A. De Vos (Alexis), S. De Baerdemacker

Physical Review A

94, 052317

2016

Abstract

Given an arbitrary 2w×2w unitary matrix U, a powerful matrix decomposition can be applied, leading to four different syntheses of a w-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. Führ and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates (w=1) to gates with arbitrary value of w. The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that U is a permutation matrix.

DOI

http://dx.doi.org/10.1103/PhysRevA.94.052317

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robotnik-resubmission-revtex.pdf

The Birkhoff theorem for unitary matrices of arbitrary dimensions

wim — Wed, 16 Nov 2016 14:53:12 +0000

S. De Baerdemacker, A. De Vos (Alexis), L. Chen, L. Yu

Linear Algebra and its Applications

514,151–164

2016

Abstract

It was shown recently that Birkho's theorem for doubly stochastic matrices
can be extended to unitary matrices with equal line sums whenever the dimension
of the matrices is prime. We prove a generalization of the Birkho
theorem for unitary matrices with equal line sums for arbitrary dimension.

DOI

http://dx.doi.org/10.1016/j.laa.2016.10.028

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birkhoff-arbitraryunitary-resubmission.pdf

Maximum probability domains for Hubbard models

claeys — Tue, 01 Mar 2016 09:55:04 +0000

G. Acke, S. De Baerdemacker, P. Claeys, M. Van Raemdonck, W. Poelmans, D. Van Neck, P. Bultinck

Molecular Physics

114 (7-8), 1392-1405

2016

Abstract

The theory of maximum probability domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond (VB) Theory-based knowledge.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1080/00268976.2016.1153742

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MolPhys.00268976.2016.1153742.pdf

Glide of dislocations in < 1 1 1 >{321} slip system: an atomistic study

wim — Fri, 12 Feb 2016 10:07:12 +0000

D. Terentyev, A. Bakaev, D. Van Neck, E. Zhurkin

Philosophical Magazine

96 (1), 71-83

2016

Abstract

Atomistic calculations are performed to investigate plastic slip in the {321} system in body-centred cubic iron. Several modern interatomic potentials, developed over the last decade, are applied to compute the stacking fault -line energy in the {321} plane and the results are compared with the ab initio prediction. The applied potentials have shown strong deviations, but several potentials acquired good qualitative agreement with the ab initio data. Depending on the applied potential, the lowest value of the Peierls stress for the edge dislocation (ED) is 50MPa (Ackland and Bacon from 1997) and the highest is 550MPa (Dudarev and Derlet from 2005), while for the screw dislocation it is much higher, in the range 1-2GPa. At finite temperature, however, the flow stress of the ED is found to decrease exponentially reaching a negligible value at about 200K, irrespective of the applied potential. On the basis of the data obtained using Ackland-Mendelev potential from 2004, we conclude that the slip resistance of the {321} system is in between the resistance of the {110} and {112} slip systems.

DOI

http://dx.doi.org/10.1080/14786435.2015.1126369

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Glide of dislocations in 1 1 1 3 2 1 slip system an atomistic study.pdf

The Birkhoff theorem for unitary matrices of prime dimension

wim — Wed, 20 Jan 2016 10:21:08 +0000

A. De Vos (Alexis), S. De Baerdemacker

Linear Algebra and its Applications

493 (2016), 455-468

2016

Abstract

The Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. We prove that any unitary matrix with equal line sums can also be written as a sum of permutation matrices (with sum of weights equal 1). Furthermore, when the matrix dimension is prime, we prove that the unitary matrix lies inside a convex complex Birkhoff polytope.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1016/j.laa.2015.12.005

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1-s2.0-S0024379515007156-main.pdf

birkhof-priem-dd20150921-metabstract.pdf

Eigenvalue-based determinants for scalar products and form factors in Richardson–Gaudin integrable models coupled to a bosonic mode

wim — Mon, 07 Dec 2015 10:18:18 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Journal of Physics A: Mathematical and Theoretical

48 (42), 425201

2015

Abstract

Starting from integrable su(2) (quasi-)spin Richardson–Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke–Jaynes–Cummings–Gaudin models and the two-channel (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke–Jaynes–Cummings–Gaudin models with the general results for RG XXZ models.

This paper has been selected as editor's pick

DOI

http://dx.doi.org/10.1088/1751-8113/48/42/425201

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15-JPhysA-48-425201-Claeys.pdf

Latest article by Pieter Claeys selected as publisher's pick by Journal of Physics A: Mathematical and Theoretical

wim — Mon, 07 Dec 2015 10:09:37 +0000

"Eigenvalue-based determinants for scalar products and form factors in Richardson–Gaudin integrable models coupled to a bosonic mode" has been selected as editor's pick by the Journal of Physics A: Mathematical and Theoretical. Read the interview with Pieter Claeys, Stijn de Baerdemacker, Mario van Raemdonck and Dimitri van Neck here.

Polynomial scaling approximations and Dynamic Correlation Corrections to Doubly Occupied Configuration Interaction wave functions

Ward — Thu, 09 Jul 2015 15:26:35 +0000

M. Van Raemdonck, D. Alcoba, W. Poelmans, S. De Baerdemacker, A. Torre, L. Lain, G. Massaccesi, D. Van Neck, P. Bultinck

Journal of Chemical Physics

143 (10), 104106

2015

Abstract

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1063/1.4930260

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1.4930260.pdf