abstract

I critically overview my research on strongly correlated fermion systems for almost five decades. It concentrated on: (i) the first derivation of what is now called the \(t\)–\(J\) model, comprising both the limit of Anderson kinetic exchange of spin–spin interaction in the Mott–Hubbard insulator and taking into account real-space pairing, subsequently applied to high-temperature superconductivity; (ii) the concept of spin-dependent heavy mass of quasiparticles in heavy-fermion systems, and (iii) the first nontrivial model of statistical thermodynamics of the Mott–Hubbard transition. Those three features, together with the specific quantum critical phenomena provide, in my view, fundamental components of the theory of strongly correlated fermions established in the 1960s. Some related questions such as introduction of atomicity in the chemical bonding (iv), and specific properties of correlated nanosystems within rigorous EDABI approach (v) are also briefly elaborated at the end.

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We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal–insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal–quantum dot–normal metal structure provide a clear signature of the presence and sign of CH interaction.

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This report contributes to the ongoing discussion on the role of structural disorder and its impact on the physical properties of strongly correlated electron systems (SCESs). It has been theoretically predicted that, in the quantum critical regime, disorder arising from structural defects or doping can significantly influence the nature of the quantum macrostate in these materials. Disorder-driven mechanisms have also been proposed to explain the non-Fermi-liquid (NFL) behavior observed in such structurally disordered systems. The most prominent among these are the Kondo disorder scenario and an alternative model based on the Griffiths phase (GP). In this review, we extend these theoretical considerations through experimental investigations, providing empirical evidence for the existence of the GP state and/or Griffiths singularities in selected SCESs. Specifically, we examine the manifestation of the GP in CeRhSn with documented atomic disorder, Fe-doped Ce\(_3\)Co\(_4\)Sn\(_{13}\) (Remeika phase), and selected Fe-based Heusler alloys.

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Many-body localization (MBL) appears to be a robust example of ergodicity breaking in many-body interacting systems. Here, we review different aspects of MBL, concentrating on various ways the disorder may be introduced into the system studied. In particular, we consider both the random and quasiperiodic diagonal (i.e. , on-site) disorders as well as bond disorder as realized in randomly distributed atoms interacting via long-range interactions. We also review the quantum sun model, which seems to be the ideal, albeit artificial, model exhibiting MBL.

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Titov and Beenakker [Phys. Rev. B 74, 041401(R) (2006)] found, by solving the Dirac–Bogoliubov–De-Gennes equation, that the product of critical current and normal-state resistance for superconductor–graphene–superconductor (S–g–S) Josephson junction takes values (for a short junction and zero temperature) between \(I_\mathrm {c}R_\mathrm {N}\approx {}2.1\) and \(I_\mathrm {c}R_\mathrm {N}\approx {}2.4\) in units of \(e/{\mit \Delta }_0\), where \({\mit \Delta }_0\) is the superconducting gap. These values are notably higher than the tunnelling bound (\(\pi /2\)), but lower than the ballistic bound (\(\pi \)). Here, we analyze the tunneling of Cooper pairs numerically through S–g–S junctions in which the longitudinal electrostatic potential profile is tuned, within gates electrodes, from a rectangular to a parabolic one. In the unipolar regime (i.e. , when the chemical potential is above the top of a barrier, \(\mu \gt 0\)), it is found that \(I_\mathrm {c}R_\mathrm {N}\) gradually evolves from the graphene-specific to the ballistic value. At the same time, the normal-state conductance increases from the sub-Sharvin value of \(1/R_\mathrm {N}\approx (\pi /4)\,G_{\mathrm {Sharvin}}\) towards to the Sharvin value \(G_{\mathrm {Sharvin}}=g_0|\mu |W/(\pi \hbar {}v_{\mathrm {F}})\), with the conductance quantum \(g_0=4e^2/h\), the junction width \(W\), and the Fermi velocity in graphene \(v_{\mathrm {F}}\). In contrast, in the tripolar regime (\(\mu \lt 0\)), both normal-state conductance and the critical current are suppressed when smoothing the potential; however, \(I_\mathrm {c}{}R_\mathrm {N}\) remains close to the graphene-specific range, even for a parabolic potential. The skewness of the current-phase relation is also discussed.

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The Friedel formula describing oscillations of the electron density due to the presence of a single impurity has been known for a long time. Here, we derive a generalized formula for the case of many impurities and we discuss in detail specific cases where few scattering centers are present. Interference patterns in the density oscillations are shown. The arguments are presented when the standard Friedel’s formula can be used additively and the inter impurity scatterings might be neglected. One can view our result as the Huygens principle applied to Friedel oscillations in many impurity cases.

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In this work, we conducted a detailed analysis of the types of mechanisms by which vortex lines interact with pinning centers generated in \(\mathrm {YBa}_2\mathrm {Cu}_3\mathrm {O}_{7-d}\) (Y123) single crystals by annealing in high oxygen pressure and Mo-substitution. Our analysis is based on the properties of these centers influencing the pinning force. Based on the previously obtained results on the dependence of the critical current density, \(j_{\mathrm {c}}\), on the magnetic field, \(j_{\mathrm {c}}(H)\), we determined \(j_{\mathrm {c}}\) as a function of temperature, \(j_{\mathrm {c}}(T)\), for different \(H\), which we used to answer the question of which pinning mechanism, \(\delta l\) or \(\delta T_{\mathrm {c}}\), dominates in Y123 single crystals. Our results differ both quantitatively and qualitatively from those previously reported, which we explain by understanding the types of pinning centers generated in studied materials. Our results provide a better understanding of the phenomena leading to significant increases in critical currents in Y123 and thus allow for better prediction of pinning centers that operate effectively under desired magnetic fields and temperatures.

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We investigate the effective interaction between two localized spin impurities embedded in a frustrated spin-\(\frac {1}{2}\) \(J_1\)–\(J_2\) Heisenberg chain. Treating the impurity spins as classical moments coupled locally to the host, we combine second-order perturbation theory with large-scale density matrix renormalization group (DMRG) calculations to determine the impurity–impurity interaction as a function of separation, coupling strength, and magnetic frustration. In the weak-coupling regime, we show that the interaction is governed by the static spin susceptibility of the host and exhibits oscillatory power-law decay in the gapless phase, modified by universal logarithmic corrections at the SU(2)-symmetric critical point. In the gapped dimerized phase, the interaction decays exponentially with distance. For intermediate and strong impurity–host coupling, we observe a crossover to a boundary-dominated regime characterized by pronounced parity effects associated with the length of the chain segment between impurities, signaling a breakdown of the simple RKKY-like description. Our results establish impurity–impurity interactions as a sensitive probe of frustrated quantum spin liquids and provide a controlled framework for distinguishing gapless and gapped phases through local perturbations.

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The ionic Hubbard model is a paradigmatic setup for studying the competition between band and Mott insulating behavior. Within the variationally exact in infinite dimensions Gutzwiller approximation, we derive a compact analytic expression for the phase boundary between the Mott and band insulators. While the method reproduces the expected band–Mott insulator phenomenology, it does not capture the correlated metallic state at finite staggered potential found, for example, in dynamical mean-field theory. This absence highlights that the metallic phase originates from incoherent Hubbard-band physics rather than Fermi-liquid behavior well captured by the Gutzwiller approximation. Our formulation establishes a concise variational framework for the ionic Hubbard model, with natural extensions to nonequilibrium setups and spin-exchange dynamics.

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The Verwey phase transition in magnetite (Fe\(_3\)O\(_4\)) exhibits a variety of phenomena that are typical of phase transformations, but in a particularly striking and pronounced form. As these phenomena and their peculiarities can be easily overlooked in the observation of other phase transitions, observing the Verwey transition, where these peculiarities are clearly visible, can draw attention to them in other phase transition studies. Important and acute phenomena showing these peculiarities include: strong dependence on doping, non-stoichiometry and defects, which can even cause a change in the character of the phase transition; the complexity of the transition, which can be predicted and observed over a wide temperature range; strong electron–electron and electron–phonon coupling; and the ability to manipulate the electronic system using a magnetic field, hydrostatic pressure or uniaxial pressure. Since these properties are typical of all solids yet accentuated in this compound and the transition is easily observable using standard and sophisticated techniques, studying it may improve our understanding of any phase transformation.

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We investigate quasiparticle states driven by the proximity effect in the quantum dot(s) coupled to superconducting samples. For the single quantum impurity, we show that its subgap spectrum consists of either the magnetically unpolarized (Andreev) or polarized (Yu–Shiba–Rusinov) bound states appearing at energies which depend on the hybridization strength with a superconductor. We also analyze the molecular bound states of the double quantum dot attached in series to a superconductor and weakly coupled to a metallic lead on the opposite side. For this setup, we show that a magnetic field is detrimental to the on-dot pairings, in much the same way as spinful impurities are pair-breakers for the Cooper pairs in conventional bulk superconductors. Finally, we address the issue of triplet pairing induced by the spin–orbit interactions in superconducting nanostructures.

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Superconductivity has recently been observed in moiré transition-metal dichalcogenide bilayers. Here, we investigate the superconducting state in twisted WSe\(_2\) using two complementary theoretical approaches. The first is based on the negative \(U\)-Hubbard model and represents a relatively conventional pairing scenario, in which strong electron–electron repulsion does not directly affect the paired state and an isotropic s-wave gap emerges. The second approach employs the \(t\)–\(J\)–\(U\) model, allowing for unconventional gap symmetries and incorporating strong correlation effects via substantial renormalization induced by the Coulomb repulsion. We compare the key properties of the superconducting states obtained within these two frameworks and discuss their implications in light of available experimental observations.

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The density functional theory calculations and tight-binding models for the doped lead apatite (and other materials in the same symmetry group) support flat bands, which could be susceptible to the emergence of various correlated phases including superconductivity. We develop a theory for the geometric contribution of the superfluid weight arising from the momentum-space topology of the Bloch wave functions of these flat bands, and we compare our results to the paradigmatic case of \(s\)-wave superconductivity on an isolated topological flat band. We show that, in contrast to the standard paradigm of flat-band superconductivity, there does not exist any lower bound for the superfluid weight in these models. Moreover, although the nontrivial quantum geometries of the normal-state bands are the same when the superconductivity appears in the ferromagnetic and paramagnetic phases, the emerging superconducting phases have very different superfluid weights. In the case of superconductivity appearing on the spin-polarized bands, the superfluid weight varies a lot as a function of model parameters. On the other hand, if the superconductivity emerges in the paramagnetic phase, the superfluid weight is robustly large and it contains a significant geometric component.

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Copper-oxide high-temperature (high-\(T_{\mathrm {c}}\)) superconductors host robust paramagnon excitations whose propagation energies are insensitive to hole concentration and correlate with maximal measured superconducting transition temperatures. Given variation of electronic structure across (and within) cuprate families, elucidation of the relationship between microscopic parameters relevant to high-\(T_{\mathrm {c}}\) superconductivity and paramagnon dynamics remains a key challenge to theory. Employing canonical Hubbard and \(t\)–\(J\)–\(U\) models of a CuO\(_2\) plane, we relate robust paramagnon energies to high-\(T_{\mathrm {c}}\) fermiology (via the ratio \(r \equiv t^\prime /|t|\) of next-nearest- to nearest-neighbor hopping integrals) and charge transfer energy, \({\mit \Delta }_{\mathrm {CT}}\). It is shown that variation of \(r\) and \({\mit \Delta }_{\mathrm {CT}}\) between materials has an opposite effect on paramagnon energy, rationalizing comparable bandwidth of magnetic excitations across multiple cuprates. Utilizing empirical values of \(r\) and \({\mit \Delta }_{\mathrm {CT}}\) as input to theory, we address magnetic dynamics in Bi-cuprate family representatives with up to three CuO\(_2\) planes, and demonstrate quantitative (within \(6\%\) margin) agreement of calculated paramagnon energies with experiment. Our work offers a route toward quantitative control of robust paramagnon physics in strongly-correlated electron systems.

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We present our novel evolutionary algorithm for generating Special Quasirandom Structures (SQS) designed to optimize the computational efficiency of Density Functional Theory (DFT) computations. Operating on the premise that symmetry proxies non-randomness, we rigorously filter out 1.P1 candidate structures prior to evaluating correlation functions. Our extinction-based workflow includes the seeding, filtration, evaluation, extinction, and repopulation phases to produce efficient supercells with maximal local environmental distinctness. We compare our results against those generated by established software packages, on the example of the \(\mathrm {W}_{70}\mathrm {Cr}_{30}\) alloy. Although standard tools achieve (marginally) lower correlation errors, our best-performing structures require approximately five times fewer unique displacements for phonon calculations. This approach sacrifices negligible quantitative disorder accuracy to significantly reduce the computational cost of modeling thermal properties.

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We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, i.e. , that of fermions with exclusion of doubly occupancy of quasimomentum states \(\{\mb k\}\) with opposite spins (\(\uparrow \downarrow \)). The second is the statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases, we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling \(n\in [0,1]\) and relative temperature \(k_\mathrm {B} T/|t|\), where \(t\lt 0\) is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band (\(n\to 1\)). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing a normal Fermi-liquid state.

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Moiré systems, such as twisted bilayer graphene or coupled layers of transition metal dichalcogenides, are considered intriguing platforms for understanding a variety of phenomena observed in strongly correlated electron systems. Here, we apply the four-band lattice model of twisted bilayer graphene to analyze whether, in the undoped case, the range of density–density interactions influences the resultant charge ordering. By using semi-classical simulated annealing optimization, as well as unrestricted Hartree–Fock calculations, we show that the pattern of order clearly depends on the range of interaction terms assumed; by performing the energy scaling with the increasing range of interactions taken into account, we select two patterns that possibly refer to the optimal charge distribution at doping \(\nu =0\) — that is, at charge neutrality in the real system.

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We present a detailed investigation of the electronic structure and bonding characteristics of hydrogen-based molecular systems (\(\mathrm {H}_2^+\), \(\mathrm {H}_2\), \(\mathrm {H}_2^-\)) using the Exact Diagonalization Ab Initio (EDABI) approach within the framework of combined first and second quantization. By analyzing the relative contributions of kinetic exchange and effective Coulomb interactions, we provide a comprehensive understanding of covalency, atomicity, and ionicity as a function of interatomic distances. Our approach leverages exact solutions of the extended Heitler–London model to quantify these interactions, extending the analysis to the discussion of properties of excited states and the dissociation limit of these molecules. The findings reveal significant differences in bonding characteristics, particularly highlighting the stability and bonding nature of the neutral \(\mathrm {H}_2\) molecule compared to its ionic counterparts. This study not only enhances our understanding of molecular interactions in hydrogen systems but also demonstrates the potential of the EDABI approach in developing more accurate computational models in quantum chemistry.

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First-principles density functional calculations were performed to calculate the physical properties of the lead-free \(\mathrm {K}_{0.5}\mathrm {Bi}_{0.5}\mathrm {TiO}_3\) and \(\mathrm {K}_{0.25}\mathrm {Sr}_{0.25} \mathrm {Bi}_{0.5}\mathrm {TiO}_3\) ferroelectric systems. In particular, the A-site cation ordering in \(\mathrm {K}_{0.25}\mathrm {Sr}_{0.25}\mathrm {Bi}_{0.5}\mathrm {TiO}_3\) and its influence on the density of electronic states were explored. The results suggest that cation ordering at A sites in \(\mathrm {K}_{0.25}\mathrm {Sr}_{0.25}\mathrm {Bi}_{0.5}\mathrm {TiO}_3\) significantly affects its density of electronic states spectra. The density of electronic states and the band structure of states for these systems were computed to determine the differences in spectra shape with respect to the band gap. It was found that in \(\mathrm {K}_{0.25}\mathrm {Sr}_{0.25}\mathrm {Bi}_{0.5}\mathrm {TiO}_3\), the band gap is larger than for the \(\mathrm {K}_{0.5}\mathrm {Bi}_{0.5}\mathrm {TiO}_3\) system by 0.2 eV. The density of electronic states and band structure spectra are required to provide reference first-principles data for further theoretical considerations and analysis of experimental spectra. The proposed calculations will also be used in the subsequent search for materials optimal for application in photovoltaics.

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We studied the electronic structure of a canonical heavy fermion superconductor CeCoIn\(_5\) using angle-resolved photoelectron spectroscopy (ARPES). We observed a non-uniform distribution of \(4f\)-derived spectral weight across the Fermi surface map measured below the coherence temperature (\(T=6~\mathrm {K} \lt T_\mathrm {coh}\approx 45\) K). Different effects of the coupling between \(4f\)-states and conduction bands were observed near the Fermi level (\(E_\mathrm {F}\)): (i) rapid change of the band slope and increasing \(4f\) spectral contribution, when approaching \(E_\mathrm {F}\), (ii) presence of heavy quasiparticle bands (\(m^{\star }\sim 100m_e\)).