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applying the DMRG algorithm and calculating the entanglement entropy, we have shown that in the anisotropic case a phase transition occurs and a Néel state emerges above a critical value of the Coulomb interaction. These findings were also corroborated by the examination of the entanglement spectrum and the spin profile of the system which clarify the structure of each phase.
Optical phonons for Peierls chains with long-range Coulomb interactions. — We have considered a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (Hückel model) induce a lattice dimerization at half band filling (Peierls effect). We have supplemented the Hückel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zigzag chains using the DMRG method. We have checked our numerical approach against analytic results for the Hückel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.
Coupled-cluster method with single and double excitations tailored by MPS wave functions. — In the last decade, the quantum chemical version of the DMRG method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable scaling, it is not suitable for computations of dynamic correlation in practice. We have presented a novel method for accurate "post-DMRG"
treatment of dynamic correlation based on the tailored CC theory, in which the DMRG method is responsible for the proper description of non-dynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We have illustrated the potential of this method on prominent multireference systems, in particular N2, Cr2 molecules and also oxo-Mn(Salen) for which we have performed the first "post-DMRG" computations in order to shed light on the energy ordering of the lowest spin states.
The correlation theory of the chemical bond. — The quantum mechanical description of the chemical bond is given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localized orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view.
For the first time, we have introduced the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and an algorithm for the multiorbital correlation clustering. These make it possible to characterize quantitatively how well a bonding picture describes the chemical system. As proof of concept, we have applied the theory for the investigation of the bond structures of several molecules. We have shown that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.
Method of Increments (MoI). — We have further developed the method of increments (MoI) that allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating whole dissociation curves. The
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reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localized and used for the many-body expansion. Therefore, in those situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot yield proper results either. We have addressed the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This led to a matrix equation where a coupling derived by the reference itself is employed. In principle, such approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as we have shown by the comparison with DMRG benchmarks. We tested this two-state constant-coupling (TSCC)-MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.
On the Multi-Reference Nature of Plutonium Oxides: PuO2+2, PuO2, PuO3 and PuO2(OH)2.
— Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. We have addressed the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the DMRG algorithm and concepts of quantum information theory. We applied the protocol to elucidate the electronic structure and bonding mechanism of volatile plutonium oxides (PuO3 and PuO2(OH)2), species associated with nuclear safety issues for which little is known about the electronic structure and energetics. We have shown how, within a scalar relativistic framework, orbital-pair correlations can be used to guide the definition of optimal active spaces which provide an accurate description of static/non-dynamic electron correlation, as well as to analyze the chemical bonding beyond a simple orbital model. From this bonding analysis, we were able to show that the addition of oxo- or hydroxo-groups to the plutonium dioxide species considerably changes the pi-bonding mechanism with respect to the bare triatomics, resulting in bent structures with considerable multi-reference character.
Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states. — Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems.
We have analyzed the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focused on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol whose performance was assessed against electronic structures obtained from DMRG reference data. Our numerical analysis covered model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG was benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicated that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method.
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Furthermore, we have examined the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.
Fermionic orbital optimization in tensor network states. — We have further developed and implemented the novel fermionic mode transformation algorithm in the Budapest QC-DMRG code and performed additional large scale calculations by keeping more than 8000 block states. For the investigated chemical systems we have obtained significantly more optimal basis sets compared to those generated by conventional approaches.
Nuclear structure theory. — We have further improved the nuclear shell variant of the DMRG algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space, utilizing various concepts of quantum information theory. We have generalized the implementation of non-Abelian symmetries.
Post-DMRG methods. —We have developed algorithms that rely on the MPS representation of the wave function obtained by the DMRG procedure. These so-called post-DMRG algorithms allow one to calculate expectation values of arbitrary operators between wave function generated by independent DMRG calculations. These methods were applied to various spin and fermionic models.
Multipartite correlations in fermionic systems. — We have started to investigate the theoretical foundations of the notions of correlations in second-quantized fermionic systems, mostly in the Jordan-Wigner representation. The results of our investigations make possible to use the main parts of the correlation theory of distinguishable systems for fermionic systems, providing firm theoretical grounds for the projects dealing with fermionic systems, e.g., in molecular physics or fermionic lattice models.
N-heterocyclic carbenes. — The N-heterocyclic carbenes are one of the most important
"experimental tools" of the modern main group chemistry, which can be applied to stabilize compounds with unidentified bonds. Nowadays, the understanding of the stabilization (whether the process is realized through dative or covalent bond) is in the focus of theoretical literature to shed light on the unidentified bonds. This year we began to study various carbenes, using our previously developed quantum information theory based analysis which is capable to distinguish covalent and dative structures.
Ultracold atomic systems. — The interest in the gas of optically trapped ultracold atoms rapidly increases due to the high controllability and tunability of the experimental setups and the versatility of the realized quantum phases. We have studied the interacting system of atoms with spin 3/2 trapped in a square lattice using different numerical approaches. In the strongly repulsive limit, the system can be described by a generalized bilinear-biquadratic Heisenberg model. We have investigated this model in terms of mean field approaches, exact diagonalization, DMRG and cluster mean field approximation. Our primary goal is to understand the conflicting results published so far for SU(4) symmetric couplings, and to extend the analysis to general cases.
Graphene nanoribbons. — We have investigated the effect of long-range interaction on graphene nanoribbons and their low-lying excitation spectrum. We have also studied triangular-shaped graphene nanoflakes to reveal the correlation effects and magnetic properties induced by the electron-electron interaction.
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Grants
“Momentum” Program of the HAS (Ö. Legeza, 2012-2017) NKFIH K120569 (Ö. Legeza, 2016-2020)
European Research Area Chemistry (OTKA NN110360, DFG SCHN 530/9-1 project under Grant No. 10041620 and FWF-E1243-N19) (Ö. Legeza, R. Schneider, F. Verstraete, 2013-2016)
International cooperation
Philipps Universität Marburg (Marburg, Germany), Optical properties of polydiacetylenes (F.
Gebhard); Entanglement scaling in momentum space DMRG (G. Ehlers, R.M. Noack)
Freie Universität (Berlin, Germany), Basis optimization using MPS based approach (C.
Krumnow, R. Schneider, J. Eisert); Ab-initio description of metal-insulator transitions (E.
Fertitta, B. Paulus)
Universität Wien (Vienna, Austria), Development of TTNS algorithm (V. Murg, F. Verstraete) Technische Universität Berlin (Berlin, Germany), Tensor factorizations in high dimensional problems (M. Pfeffer, R. Schneider)
McMaster University (McMaster, Canada), Bond breaking and formation through entanglement (K. Boguslawski, P. Tecmer, P. Ayers)
Ustav Fyzikalni Chemie J. Heyrovskeho AV CR (Praha, Czech Republic), Development of the quantum chemistry version of the DMRG-TCCD method (L. Veis, J. Pittner)
Universidad Autonoma de Madrid, and Instituto de Estructura de la Materia, CSIC (Madrid, Spain), Development of the nuclear shell version of the DMRG method (A. Poves, J.
Dukelsky)
Publications
Articles
1. Boguslawski K, Tecmer P, Legeza Ö: Analysis of two-orbital correlations in wave functions restricted to electron-pair states. PHYS REV B 94:(15) 155126/1-8 (2016) 2. Hagymási I, Legeza Ö: Characterization of a correlated topological Kondo insulator in
one dimension. PHYS REV B 93:(16) 165104/1-6 (2016)
3. Hagymási I, Legeza Ö: Entanglement, excitations, and correlation effects in narrow zigzag graphene nanoribbons. PHYS REV B 94:(16) 165147/1-8 (2016)
4. Krumnow C, Veis L, Legeza Ö, Eisert J: Fermionic orbital optimization in tensor network states. PHYS REV LETTERS 117:(21) 210402/1-6 (2016)
5. Timár M, Barcza G, Gebhard F, Veis L, Legeza Ö: Hückel-Hubbard-Ohno modeling of π-bonds in ethene and ethyne with application to trans-polyacetylene. PHYS CHEM CHEM PHYS 18:(28) 18835-18845 (2016)
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6. Veis L, Antalík A, Brabec J, Neese F, Legeza O, Pittner J: Coupled cluster method with single and double excitations tailored by matrix product state wave functions. J PHYS CHEM LETTERS 7:(20) 4072-4078 (2016)
Other
7. Sólyom J, Zaránd G: A kvantumtérelmélettől a szilárdtest-fizikáig. Zawadowski Alfréd tudományos életútja (From Quantum field theory to Solid State Physics. The scientific carreer of Alfréd Zawadowski, in Hungarian). FIZIKAI SZEMLE 66:(5) 146-150 (2016)
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