csirik

• Bakkestuen, Vebjørn Hallberg; Csirik, Mihaly Andras; Laestadius, Andre & Penz, Markus (2025). Density-Functional Theory for the Dicke Hamiltonian. Journal of statistical physics. ISSN 0022-4715. 192(5). doi: 10.1007/s10955-025-03442-9. Full text in Research Archive Show summary

  A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a Hohenberg-Kohn theorem that manifests the magnetization and displacement as internal variables, along with several representability results. The constrained-search functionals for pure states and ensembles are introduced and analyzed. We find the optimizers for the pure-state constrained-search functional to be low-lying eigenstates of the Hamiltonian and, based on the properties of the optimizers, we formulate an adiabatic-connection formula. In the reduced case of the Rabi model we can even show differentiability of the universal density functional, which amounts to unique pure-state v-representability.

• Tancogne-Dejean, Nicolas; Penz, Markus; Laestadius, Andre; Csirik, Mihaly Andras; Ruggenthaler, Michael & Rubio, Angel (2024). Exchange energies with forces in density-functional theory. Journal of Chemical Physics. ISSN 0021-9606. 160(2), p. 024103–024103. doi: 10.1063/5.0177346. Full text in Research Archive Show summary

  We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange–correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn–Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.

• Csirik, Mihaly Andras; Laestadius, Andre & Tellgren, Erik (2024). Thermodynamic limit for the magnetic uniform electron gas and representability of density-current pairs. Journal of Mathematical Physics. ISSN 0022-2488. 65(11). doi: 10.1063/5.0198786. Full text in Research Archive Show summary

  Although the concept of the uniform electron gas is essential to quantum physics, it has only been defined recently in a rigorous manner by Lewin, Lieb and Seiringer. We extend their approach to include the magnetic case, by which we mean that the vorticity of the gas is also held constant. Our definition involves the grand-canonical version of the universal functional introduced by Vignale and Rasolt in the context of current-density-functional theory. Besides establishing the existence of the thermodynamic limit, we derive an estimate on the kinetic energy functional that also gives a convenient answer to the (mixed) current-density representability problem.

• Laestadius, Andre; Csirik, Mihaly Andras; Penz, Markus; Tancogne-Dejean, Nicolas; Ruggenthaler, Michael & Rubio, Angel [Show all 7 contributors for this article] (2024). Exchange-only virial relation from the adiabatic connection. Journal of Chemical Physics. ISSN 0021-9606. 160(8). doi: 10.1063/5.0184934. Full text in Research Archive Show summary

  The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength λ at λ = 0. This agrees with the Levy–Perdew definition of the exchange energy as a high-density limit of the full exchange–correlation energy. By relying on v-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit (λ ↘ 0) involving the exchange–correlation potential vλ xc, which exists by assumption of v-representability. On the other hand, a local-exchange potential vx is not warranted to exist as such a limit.

• Penz, Markus; Tellgren, Erik Ingemar; Csirik, Mihaly Andras; Ruggenthaler, Michael & Laestadius, Andre (2023). The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory. ACS Physical Chemistry Au. 3(4), p. 334–347. doi: 10.1021/acsphyschemau.2c00069. Full text in Research Archive Show summary

  The Hohenberg–Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg–Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg–Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.

• Faulstich, Fabian M.; Kristiansen, Håkon Emil; Csirik, Mihaly Andras; Kvaal, Simen; Pedersen, Thomas Bondo & Laestadius, Andre (2023). The S-diagnostic - an a posteriori error assessment for single-reference coupled-cluster methods. Journal of Physical Chemistry A. ISSN 1089-5639. 127(43), p. 9106–9120. doi: 10.1021/acs.jpca.3c01575. Full text in Research Archive Show summary

  We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+. Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T1, D1, and D2 diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T1, D1, and D2 diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multi-reference regimes. The S-diagnostic moreover correctly detects the successful SRCC computations for [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+, which have been known to be misdiagnosed by T1 and D1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

• Csirik, Mihaly Andras & Laestadius, Andre (2023). Coupled-Cluster theory revisited: Part I: Discretization. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). ISSN 2822-7840. 57(2), p. 645–670. doi: 10.1051/m2an/2022094. Full text in Research Archive Show summary

  In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. These methods aim at accurately solving the many-body Schrödinger equation. In this first part, we rigorously describe the discretization schemes involved in Coupled-Cluster methods using graph-based concepts. This allows us to discuss different methods in a unified and more transparent manner, including multireference methods. Moreover, we derive the single-reference and the Jeziorski–Monkhorst multireference Coupled-Cluster equations in a unified and rigorous manner.

• Csirik, Mihaly Andras & Laestadius, Andre (2023). Coupled-Cluster theory revisited: Part II: Analysis of the single-reference Coupled-Cluster equations. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). ISSN 2822-7840. 57(2), p. 545–583. doi: 10.1051/m2an/2022099. Full text in Research Archive Show summary

  In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative information about the solutions of these equations that also sheds light of the numerically observed behavior. In particular, we compute the topological index of the zeros of the single-reference Coupled-Cluster mapping. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schrödinger equation.

• Penz, Markus; Tellgren, Erik Ingemar; Csirik, Mihaly Andras; Ruggenthaler, Michael & Laestadius, Andre (2023). The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields. ACS Physical Chemistry Au. doi: 10.1021/acsphyschemau.3c00006. Full text in Research Archive Show summary

  TheHohenberg−Kohntheoremof density-functionaltheory(DFT)is broadlyconsideredtheconceptualbasisfora fullcharacterizationof an electronicsystemin its groundstateby justone-bodyparticledensity.In thisPartII of a seriesof twoarticles,weaimat clarifyingthestatusof thistheoremwithindifferentextensionsofDFTincludingmagneticfields.Wewillin particulardiscusscurrent-density-functionaltheory(CDFT)andreviewthedifferentformulationsknownintheliterature,includingtheconventionalparamagneticCDFTandsomenonstandardalternatives.Fortheformer,it is knownthattheHohenberg−Kohntheoremis nolongervaliddueto counterexamples.Nonetheless,paramagneticCDFThasthemathematicalframeworkclosestto standardDFTand,justlikein standardDFT,nondifferentiabilityof thedensityfunctionalcanbe mitigatedthroughMoreau−Yosidaregularization.Interestinginsightscanbe drawnfrombothMaxwell−SchrödingerDFTandquantum-electrodynamicDFT,whicharealsodiscussedhere.

• Penz, Markus; Csirik, Mihaly Andras & Laestadius, Andre (2023). Density-potential inversion from Moreau-Yosida regularization. Electronic Structure. 5(1). doi: 10.1088/2516-1075/acc626. Full text in Research Archive Show summary

  For a quantum-mechanical many-electron system, given a density, the Zhao–Morrison–Parr method allows to compute the effective potential that yields precisely that density. In this work, we demonstrate how this and similar inversion procedures mathematically relate to the Moreau–Yosida regularization of density functionals on Banach spaces. It is shown that these inversion procedures can in fact be understood as a limit process as the regularization parameter approaches zero. This sheds new insight on the role of Moreau–Yosida regularization in density-functional theory and allows to systematically improve density-potential inversion. Our results apply to the Kohn–Sham setting with fractional occupation that determines an effective one-body potential that in turn reproduces an interacting density.

• Homa, G.; Csordás, A.; Csirik, Mihály András & Bernád, J.Z. (2020). Range of applicability of the Hu-Paz-Zhang master equation. Physical Review A (PRA). ISSN 2469-9926. 102(2). doi: 10.1103/PhysRevA.102.022206. Full text in Research Archive

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• Laestadius, Andre; Penz, Markus; Csirik, Mihaly Andras; Herbst, Michael F. & Bakkestuen, Vebjørn Hallberg (2025). Using Moreau-Yosida regularization in density-functional theory. Full text in Research Archive
• Csirik, Mihaly Andras & Laestadius, Andre (2022). Topological Index and Homotopy in Coupled-Cluster theory. Full text in Research Archive Show summary

  We propose a comprehensive mathematical framework for Coupled-Cluster-type methods based on topological degree theory. This allows us to establish more general existence results than Schneider's and deduce local information about the solutions of the CC equations. The idea of constructing a homotopy for CC theory is not new, and has been extensively studied in the past. We consider the more recent Kowalski--Piecuch (KP) homotopy from a mathematical point of view and use it as a theoretical tool to prove the existence of a truncated CC solution. This follows from a more general result guaranteeing the existence of a whole solution curve of the KP homotopy.

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