stuff was going on #2015

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2015

• 12 aug 2015 :: Benjamin Maveau and Matthias Meeuws have succesfully defended their MSc thesis at the CMM on Richardson-Gaudin integrable systems at the end of June.

  • Benjamin's MSc thesis was on Richardson-Gaudin integrability for bosonic quantum many-body systems, with applications, to several physical systems where bosonic pairing is present, either in a mathematical sense via a Schwinger representation (such as the asymmetric quantum rotor), or in a physical sense (such as in Arima & Iachello's Interacting Boson Model).

    The solver is based on a pseudo-deformation of the su(1,1) quasispin algebra, and can handle xxx (rational) as well as xxz (hyperbolic/trigonometric) integrable models. In sharp contrast to the su(2) pairing models, there is a one-to-one correspondence between the Bethe Ansatz states and the collective Tamm-Dancoff states in the contraction limit of the quasispin. However, the real-to-complex singularities persist for the xxz systems, so Benjamin had to pull a few tricks from his numerical toolbox to produce some cool plots.

    

    This plot is a typical evolution of the (real part) of the rapidities of a 2-level bosonic integrable Richardson-Gaudin model with xxz interactions for increasing interaction strength. The blue lines are the typical Moore-Read/Read-Green condensate points also encountered in fermionic pairing models.

  • Matthias investigated the connection between su(2) Richardson-Gaudin and their mean-field analogon in Mean-field theory for the conserved charges in Richardson-Gaudin models. Matthias found that the Richardson-Gaudin conserved charges remain in involution at the mean-field level. This means that the Bardeen-Cooper-Schrieffer (BCS) equations are equivalent for all conserved charges, giving rise to the same BCS solution. An interesting result is that the coherent BCS solution only approximates the ground state of one of the conserved charges, so that is why Matthias investigated systematic improvements on top of the BCS state using an Equations of Motions technique from Alexander Volya & Vladimir Zelevinsky, with promising results.

• 09 aug 2015 :: My 3rd year as a painter just went by ...

• 18 jun 2015 :: On a vaguely related note: Intrigued by the big data hype, I started reading Nicholas Carr's "The Glass cage: where automation is taking us", and wanted to know more. That's why I attended a course on Data Mining at Ghent University's IPVW. Moreover, I took part in the exam and .... passed, yay!

• 16 jun 2015 :: The Dicke model (and therefore also the Jaynes-Cummings limit), is an integrable model that can be linked to the su(2) Richardson-Gaudin (RG) integrable models via a suitable bosonization procedure (be it a holstein-primakoff expansion, or a pseudo-deformation of the su(2) algebra, etc.). Tschirhart and Faribault found out that the Dicke model can also be expressed in the "Eigenvalue-based" variables, just like the su(2) RG systems. In a paper on the arxiv, we show how we can rederive their results in a very short and straightforward way, starting from the expressions we have derived recently for the su(2) XXZ models, and bringing them to the Dicke model via the pseudo-deformation. In addition, we show how these results can be naturally extended to other su(2) models coupled to a bosonic mode, like the extended (p+ip)-wave model, initially introduced by Clare Dunning and collaborators.

• 02 jun 2015 :: I will be in Beijing next week for the ICQC15 meeting, probably the biggest event for theoretical chemists all year. There will be a large delegation of the Gemini, including (invited speaker) Paul Ayers, and (poster presenters) Paweł, Kasia, & yours truly. My poster

  

  will be presented in poster session I. I will talk about a variational Richardson-Gaudin approach for non-integrable quantum many-particle systems exhibiting collective and non-collective pairing correlations. Please come over, and say hi!

• 27 may 2015 :: update in the art section

• 25 may 2015 :: This just in: two tokens of appreciation!

  • The first one is a collective one for the article we published with Peter Limacher in Molecular Physics. In this article, we investigate the effect of the pairing scheme on the energy of a doubly-occupied configuration interaction (DOCI) wavefunction, aka the orbital optimization scheme (OO). Among others, we calculated the energy landscape of the H₄ molecule in D4h symmetry (in a minimal basis set, to keep things as simple as possible). The landscape is full of local extrema (minima/maxima/saddle points), including the following 10 configurations

    

    Each square represents an orbital (as a linear combination of the 4 localized orbitals on the corners on the H₄) with the magnitude given by the radius of the circle. Probably more important than the global minimum configuration (configuration (V) is clearly the global minimum), is the fact that there exist many global minima. The spotlights were shun by a virtual issue, an editor's selection of articles spanning the years 2013-2015. Thank you very much, MolPhys!

  • The second token of appreciation is a personal one by my Physics Engineering students of "Quantum mechanics II". In the last course evaluation, special mention was given to the TA (i.e.: yours faithful!), who is "very well appreciated by the students" (with some nice personal remarks and comments to back that up). It is heart warming to see that my strong dedication to teaching is being picked up by my students.

• 04 may 2015 :: Sebastian Wouters published an update to his CheMPS2 code in Computer Physics Communications. As the title suggests, it contains an improved Self-Consistent Field solver based on an Direct Inversion of the Iterative Subspace (DIIS), an orbital localizer and there is access to correlation functions.

• 15 apr 2015 :: The greatest change in the past few months, is that I finally turned into a (quantum) chemist, which has been predicted (retroactively) by UGent's new software algoritme simon, a new online tool that helps you deciding which major you should take in bio-engineering. Anyway, and what about all other things? Well...

  • Pieter Claeys just published his first full research paper in Physical Review B. We show in this paper that the set eigenvalue-based Richardson-Gaudin (RG) equations, introduced by Alexandre Faribault and collaborators, can be extended from XXX (RG) models to XXZ in a very elegant way. The eigenvalue-based RG equations suffer not from the singularities in the original RG equations with the rapidities as variables. I am very excited about these new developments in the numerical department of integrability.

    

    The figure (which appears in the paper) shows the real part (2nd row) and imaginary part (3rd row) of the Richardson-Gaudin rapidities of three different integrable models (colums), corresponding to a rational (xxx, Γ=0, 1st column), hyperbolic (xxz, Γ<0, 2nd column) and trigonometric (xxz, Γ>0, 3rd column) case as a function of the interaction strength g. One can see the singular values of g where the RG rapidities recombine into complex conjugate pairs (or vice versa). Clearly, the eigenvalue-based variables (1st row) do not suffer from these singularites at all.

  • Paul Johnson has successfully defended his PhD thesis, and is now officially a McMaster-UGent joint PhD. Congrats! Paul moved to Houston to work in Gustavo Scuseria's group at Rice University.

  • I attended the GROUP30 conference in Ghent, presenting the MSc thesis results of Pieter Claeys on the Dicke model, which have now been published in the proceedings. Alexis De Vos also presented some of our U=ZXZ results, based on our proven matrix scaling conjecture, and also made it into the proceedings as well. The proceedings are open access, so check it out!

  • More news on the orbital optimization (OO) front! In collaboration with the McMaster Gemini Clan, we developed a OO scheme based on a generalized Brillouin theorem for Hartree-Fock theory. Many applications are presented in this publication, including cyclobutadiene, the BeH₂ molecule, and benzene. Note that the benzene AP1roG calculations were performed with 42 electrons in 138 orbitals.

  • Our conjecture with Alexis De Vos on the Scaling of Unitary Matrices, aka Sinkhorn's theorem for Unitary matrices, has been published in Open Systems & Information Dynamics, and moreover (!), it has been proven by Martin Idel & Michael Wolf of the Technische Universitaet Muenchen. They used a non-constructive proof for the conjecture, showing that this problem is a special case of the Arnold conjecture on the intersection of Lagrangian submanifolds. Nice!

2014

• 30 jun 2014 :: There has just been too much going on the last few months, so here is a snippit

  • Mario's paper on the XXZ Richardson-Gaudin model, which appeared on the arXiv on feb 4th 2014, has been published in Physical Review B.

  • The same journal saw the publication of our paper with Katharina Boguslawski and Paweł Tecmer about AP1roG for the 1d Hubbard model (and related hydrogen chains) as a rapid.

  • I mentioned earlier (see 03 feb 2014) that the orbital optimization is crucial for the of geminal and/or DOCI approaches. In a nice publication in the Journal of Chemical Physics with the McMaster collaboration, we discuss how this optimisation can be performed invoking the concept of seniority.

  • It felt rather particular to file my old passport for a meticulous one, as the old one had so many memories stamped and glued in. Anyway, I was in Telluride, CO for the more than exciting Low-scaling and Unconventional Electronic Structure Techniques Conference in the Ah Haa School for the Arts . This place brought the finest of what quantum chemistry can offer nowadays, including -Aha!- a considerable Ghentonian delegation :-). I presented some preliminary results of using the full set of Richardson-Gaudin states for a DOCI bases for a very attentive audience. More news on this topic to be expected soon!

  • My long-time collaborator and favorite moustache Alexis De Vos has presented some of our findings on the decomposition of a quantum circuit with NEGATOR gates at the International Symposium on Multi-Valued Logic 2014 in Bremen. In this contribution, we proved our conjecture for a particular subset of unitary matrices. The paper will appear in the proceedings soon.

  • Last but not least: Pieter Claeys has succesfully defended his MSc thesis on Integrable quantum many-body systems: Properties and extensions of the Dicke Model, and the introduction of time dependence. Beside a very nice introduction into Richardson-Gaudin integrability for interacting atom-photon systems (via a pseudo-deformation of the quasispin algebra), it discusses some features within the Heine-Stieltjes connection, a Richardson-Gaudin-Dicke solver, and introduces a few generalisations, such as time-dependence of the Schrödinger Equation. Pieter will join our research unit on fundamental quantum many-body physics at the Center for Molecular Modeling with an FWO-Vlaanderen pre-doctoral fellowship.

  • and oh yes: we had the annual opendeurdag at the DKO, but that's something for the art corner :-)

• 07 mar 2014 :: Good news today: the arXiv paper by Brecht Verstichel (see 08 jul 2013)in which we impose sub-cluster constraints on the 2-body density matrix of the 2d hubbard model in a variational 2-body density matrix approach has been published today in Eur. Phys. J. B.

• 27 feb 2014 :: Dynamical correlations with APIG wavefunctions: a nice paper with the McMaster collaboration appeared in PCCP, where we presented a multi-reference perturbation theoretic framework developed by Kobayashi and collaborators to capture dynamical correlations in the AP1roG geminal wavefunctions. Calculations are presented for N₂ and H₂O.

• 04 feb 2014 :: 3 days in a row, 3 arXiv posts. Today, there's a paper by PhD student Mario Van Raemdonck, employing the pseudo-deformation algebra I introduced here to solve and investigate the Richardson-Gaudin equations of the factorisable XXZ Hamiltonian. Among other things, it allows us to study the gap closure at the Read-Green point, and the behaviour of the Richardson-Gaudin variables around the Moore-Read condensation point.

• 03 feb 2014 :: Today, Katharina Boguslawski and Paweł Tecmer of the chemistry collaboration put a paper on the arXiv, discussing the performance of our recently introduced AP1roG for 1D hydrogen chains and Hubbard models with single-orbital orbital optimization. Turns out the orbital optimization is crucial to get the correlation energy right! This is equivalent to saying that the optimal pairing scheme is not necessarily the one dictated by Hartree-Fock theory, the Natural Orbitals, etc.

• 31 jan 2014 :: Alexis De Vos and yours faithful have put a paper on the arxiv about the scaling of Unitary matrices. We wanted to know whether it was possible to "scale" a unitary matrix U(n) with two diagonal matrices L and R, such that LUR=V gives a unitary matrix V, where V has equal line sums (i.e. the sum of the rows and columns all equal the same complex number. After some serious investigations, we could not come up with a solid proof (except for n=2, and some restricted classes of U(n)), however our approach based on a variation of the sinkhorn algorithm points towards a conjecture. Any comments are welcome.

2013

• 28 nov 2013 :: And now for something completely different. I'm a 2nd year DKO (i.e. part-time) student at the Academie voor Beeldende Kunsten in Ghent (Academy for Visual Arts), in the painting section under supervision of Annique Mahieu. This month, I had my very first group exhibition, organised by the Koninklijke Bond van het Personeel of UGent and UZ Gent. There were was a lot of nice stuff to be seen, including my small oils on MDF (picture 105 :-))

• 06 nov 2013 :: It has been a busy summer, with quite some travelling. I have been to the 7th Molecular Quantum Mechanics 2013 meeting in Lugano (Switzerland), the XXInd International Conference on Integrable Systems and Quantum symmetries in Kafka's Prague (Czech Republic), and the XX International School on Nuclear Physics, Neutron Physics and Applications in Varna (Bulgaria). In both meetings, I got to present some of our work on Richardson-Gaudin integrability, talking about Geminals in Lugano, pseudo-deformations in Prague and superfluid nuclei in Varna. The proceedings for the latter meeting have been posted on the arXiv a few days back. They talk about pairing corelations between the neutrons in the Sn isotopes, using a simple Woods-Saxon + Richardson pairing model. The behaviour of the Richardson rapidities througout the chain of isotopes displays a sub-shell structure that has been reported previously.

• 08 jul 2013 :: my fellow FWO-Fellow Brecht Verstichel has put a paper on the arXiv, talking about (extended) cluster constraints for the variatonal 2-body Density Matrix (v2DM) optimalisation of the 2d hubbard model. The idea is to use the exact information of 2x2 and 3x3 clusters within a larger lattice as a constraint, and also allow for a coupling with the rest of the lattice. These constraints are cheaper than the 3-body constraints.

• 16 may 2013 :: shadokistan is no longer accessible for wanderers of the world wild web, but I moved it to the good'ol allserv server of ugent.

• 22 mar 2013 :: (quantum) computing this time: the journal Open Systems & Information Dynamics has published a paper by Alexis De Vos and your humble servant on the NEGATOR gate. The NEGATOR can be regarded as a one-parameter group of phase-corrected qubit rotations around the x-axis (the σ_x pauli matrix), such that it contains the NOT gate. It generates the XU(2) group, which is the group of 2x2 unitary matrices with equal line sums. Adding a CNOT to the NEGATOR generates general XU(n) groups with n=2^w.

• 12 mar 2013 :: Some more news on the chemistry side: There is a paper out at JCTC with Peter Limacher's recent projected Schrodinger equation calculations with AP1roG. It's one of the flavours of geminals we (i.e. the authors of the mentioned paper) are currently exploring for strongly-correlated quantum chemistry. Some of the phenomena we looked at is the bond dissociation of linear H₂ chains.

• 12 feb 2013 :: The preprint paper on the effect of impurities on the superconducting ground state of Al nanograins, by Mario, Dimitri, and myself has been published this week in a topical issue of Eur. Phys. J. D.

• 11 jan 2013 :: Next week, I will be at the Institute of Theoretical Physics of the University of Amsterdam, visiting Jean-Sébastien Caux, to work further on our joint research program on Richardson-Gaudin correlation functions.

• 02 jan 2013 :: The new year brought a publication in a field that is equally new for me: quantum chemistry. In this publication, written for the Reduced Density Matrices: A Simpler Approach to Many-Electron Problems? issue of Comp. Theor. Phys. in honor of John Coleman, we (that is: Paul Johnson, Paul Ayers, and Peter Limacher from McMaster University, Patrick Bultinck from UGent's quantum chemistry group and Dimitri Van Neck and your humble servant from the CMM at UGent) present a new class of non-orthogonal geminals for the description of static correlations in quantum chemical systems. It's rather technical, but applications are to be expected soon!

2012

• 01 nov 2012 :: There is a new preprint paper by Mario Van Raemdonck, Dimitri Van Neck and your humble servant on the arxiv. We used a simple particle-in-a-box model to investigate the effect of geometry and impurities on the pair condensation energy of superconducting nanograins. The paper has been submitted to a special issue of Eur. Phys. J. D for the International Symposium on Small Particles and Inorganic Clusters I attended recently (cfr. 8 jul 2012).

• 25 oct 2012 :: That paper I put recently (6 aug 2012) on the arxiv., where I related the singular interaction strengths of the Richardson-Gaudin equations to the collective nature of the multiphonon states in the Tamm-Dancoff Approximation, has been published today by Phys. Rev. C.

• 10 oct 2012 :: Merely back at home, I got to attend the very interesting Discussion day on exchange-correlation and chemical bonding organised by Patrick Bultinck's quantum chemistry group at Ghent University, and the following days, I will be attending the Quantum Physics and Logic 2012 workshop at the ULB in Brussels. My close collaborator Alexis De Vos of the Department of Electronics and Information Systems will be presenting some of our findings concerning SQRT(NOT) gates.

• 28 sep 2012 :: Next week, I will be in la dolce italia, visiting dr. Lorenzo Fortunato of the University of Padova & INFN. My PhD thesis was on the Bohr-Mottelson Collective Model, for which I designed an algebraic Cartan-Weyl formulation, and developed a couple of analytic models for triaxial nuclei. The latter was done in close collaboration with Lorenzo. It will be nice to be back at the alma mater of copernicus and galilei. Naturalmente, you are most welcome to attend my seminar (on monday, I guess), it will be on Richardson-Gaudin integrability.

• 30 aug 2012 :: I will be presenting this talk at the Quantum Integrable Systems & Geometry workshop in Olhão. It will mainly be about the singular Richardson-Gaudin equations and how these relate to the Tamm-Dancoff Approximations, like described in that paper I put recently (6 aug 2012) on the arxiv. Portugal is a first-timer for me, pretty excited.

• 6 aug 2012 :: The non-linear Richardson-Gaudin equations are plagued by singularities. In a paper on the arxiv, I show how the singularities are related to the structure of the Bethe Ansatz wavefunctions in the contraction of the quasispin. In addition, the construction can be regarded as a potentially fast and simple Richardson solver (such as in Mario's MSc thesis or this and this paper).

• 8 jul 2012 :: I will be presenting this poster at the International Symposium on Small Particles and Inorganic Clusters, held at one of the oldest centers of knowledge in western europe

• 26 jun 2012 :: Mario Van Raemdonck has defended his MSc thesis on Invloed van de geometrie op de supergeleidende toestand in metaalachtige nanokorrels (The influence of geometry on the superconducting state of metallic nanograins). Here is a copy of his thesis(dutch).

• 30 may 2012 :: The conference proceedings of the XIX International School on Nuclear Physics, Neutron Physics and Applications have been published in the Journal of Physics: Conference Series , including my contribution on the Richardson-Gaudin equations in the contraction limit of the su(2) quasi spin