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Abstract The sustained interest in investigating magnetism in the 2D limit of insulating antiferromagnets is driven by the possibilities of discovering, or engineering, novel magnetic phases through layer stacking. However, due to the difficulty of directly measuring magnetic interactions in 2D antiferromagnets, it is not yet understood how intralayer magnetic interactions in insulating, strongly correlated, materials can be modified through layer proximity. Herein, the impact of reduced dimensionality in the model van der Waals antiferromagnet NiPS3 is explored by measuring electronic excitations in exfoliated samples using Resonant Inelastic X‐ray Scattering (RIXS). The resulting spectra shows systematic broadening of NiS6 multiplet excitations with decreasing layer count from bulk down to three atomic layers (3L). It is shown that these trends originate from a decrease in transition metal‐ligand and ligand–ligand hopping integrals, and by charge‐transfer energy evolving from Δ = 0.83 eV in the bulk to 0.37 eV in 3L NiPS3. Relevant intralayer magnetic exchange integrals computed from the electronic parameters exhibit a decrease in the average interaction strength with thickness. This study underscores the influence of interlayer electronic interactions on intralayer ones in insulating magnets, indicating that magnetic Hamiltonians in few‐layer insulating magnets can greatly deviate from their bulk counterparts.

The features of materials leading to the strong correlation effect and the phenomena realized in them are considered: the metal-insulator Mott transition and high-temperature superconductivity. The history of their study is traced. Particular attention is paid to studying the role of the interorbital correlation effect and the Hund's coupling in multiorbital systems as well as the electron-phonon interaction in systems with strong Coulomb interaction. The development of the strong coupling diagram technique is analyzed and the results obtained based on the approach used are presented. [ABSTRACT FROM AUTHOR]

We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier-obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree–Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier-obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest-neighbor orbital overlap g, this model exhibits stable ferromagnetism up to a finite bandwidth W ∼ U g , where U is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier-obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier-obstructed bands. [ABSTRACT FROM AUTHOR]

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript, we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spinpolarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments. [ABSTRACT FROM AUTHOR]

Neuromorphic computing-which aims to mimic the collective and emergent behavior of the brain's neurons, synapses, axons, and dendrites-offers an intriguing, potentially disruptive solution to society's ever-growing computational needs. Although much progress has been made in designing circuit elements that mimic the behavior of neurons and synapses, challenges remain in designing networks of elements that feature a collective response behavior. We present simulations of networks of circuits and devices based on superconducting and Mott-insulating oxides that display a multiplicity of emergent states that depend on the spatial configuration of the network. Our proposed network designs are based on experimentally known ways of tuning the properties of these oxides using light ions. We show how neuronal and synaptic behavior can be achieved with arrays of superconducting Josephson junction loops, all within the same device. We also show how a multiplicity of synaptic states could be achieved by designing arrays of devices based on hydrogenated rare earth nickelates. Together, our results demonstrate a research platform that utilizes the collective macroscopic properties of quantum materials to mimic the emergent behavior found in biological systems.

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These notes are based on lectures serving the advanced graduate education of the Delta Institute of Theoretical Physics in the Netherlands in autumn 2021. The goal is to explain in a language that can be understood by non-specialists' very recent advances in quantum information and especially string theory suggesting the existence of entirely new forms of matter. These are metallic states characterized by an extremely dense many-body entanglement, requiring the supremacy of the quantum computer to be completely enumerated. The holographic duality discovered in string theory appears to be a mathematical machinery capable of computing observable properties of such matter, suggesting the presence of universal general principles governing its phenomenology. The case is developing that these principles may well apply to the highly mysterious physical properties observed in the high-temperature superconductors and other strongly interacting electron systems of condensed matter physics. [ABSTRACT FROM AUTHOR]

Effective Hamiltonian of Crystal Field (EHCF) is a hybrid quantum chemical method originally developed for an accurate treatment of highly correlated d-shells in molecular complexes of transition metals. In the present work, we generalise the EHCF method to periodic systems containing transition metal atoms with isolated d-shells, either as a part of their crystal structure or as point defects. A general solution is achieved by expressing the effective resonance interactions of an isolated d-shell with the band structure of the crystal in terms of the Green's functions represented in the basis of local atomic orbitals. Such representation can be obtained for perfect crystals and for periodic systems containing atomic scale defects. Our test results for transition metal oxides (MnO, FeO, CoO, and NiO) and MgO periodic solid containing transition metal impurities demonstrate the ability of the EHCF method to accurately reproduce the spin multiplicity and spatial symmetry of the ground state. For the studied materials, these results are in a good agreement with experimentally observed d-d transitions in optical spectra. The proposed method is discussed in the context of modern solid state quantum chemistry and physics. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of computing fermion propagators in a broad variety of strongly correlated systems that can be mapped onto the theory of fermions coupled to an (over)damped bosonic mode. A number of the previously applied approaches and their results are reviewed, including the conventional diagrammatic resummation and eikonal technique, as well as the 'experimental' higher-dimensional bosonization and generalized (i.e. 'bottom-up' or 'non-AdS/non-CFT') holographic conjecture. It appears that, by and large, those results remain either in conflict or incomplete, thereby suggesting that the ultimate solution to this ubiquitous problem is yet to be found. [ABSTRACT FROM AUTHOR]

An epitaxial film of YbFe2O4, a candidate for oxide electronic ferroelectrics, was fabricated on yttrium-stabilized zirconia (YSZ) substrate by magnetron sputtering technique. For the film, second harmonic generation (SHG), and a terahertz radiation signal were observed at room temperature, confirming a polar structure of the film. The azimuth angle dependence of SHG shows four leaves-like profiles and is almost identical to that in a bulk single crystal. Based on tensor analyses of the SHG profiles, we could reveal the polarization structure and the relationship between the film structure of YbFe2O4 and the crystal axes of the YSZ substrate. The observed terahertz pulse showed anisotropic polarization dependence consistent with the SHG measurement, and the intensity of the emitted terahertz pulse reached about 9.2% of that emitted from ZnTe, a typical nonlinear crystal, implying that YbFe2O4 can be applied as a terahertz wave generator in which the direction of the electric field can be easily switched. [ABSTRACT FROM AUTHOR]

We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier-obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree–Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier-obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest-neighbor orbital overlap g, this model exhibits stable ferromagnetism up to a finite bandwidth W∼Ug, where U is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier-obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier-obstructed bands.

One of the most powerful and popular quantum entanglement-based computation methods for the simulation of one-dimensional and quasi-two-dimensional strongly correlated materials is the Density Matrix Renormalization Group (DMRG) technique. A lower quantum entanglement between the system’s degrees of freedom will result in a higher accuracy of the method. However, quantum entanglement between two complementary subsystems of a closed system depends on how the degrees of freedom have been distributed between them, and therefore, it is not in general invariant under arbitrary unitary transformations. Entanglement is invariant only under those unitary transformations which do not mix the degrees of freedom associated with the two subsystems. Consequently, a fundamental question is that if it is possible to construct, algorithmically, unitary transformations which minimize entanglement between degrees of freedom of the system and therefore maximize the DMRG technique? A general solution to this problem is highly nontrivial in general. In this paper, we study interacting fermionic models and by considering single-particle unitary transformations only. We define a novel and efficient method to find the optimal single-particle unitary transformations. In this framework, we show that using our algorithm, the accuracy of the DMRG method at a given bond dimension is increased and the ground-state energy is decreased and approaches to its exact value. Our method paves the way toward finding more general (many-particle) optimized unitary transformations and helps us to better understand the behavior of fermions in strongly correlated materials.

We consider a Cooper pair beam splitter for an iron-pnictide superconductor and calculate the entangled electron-hole current. We investigate the interplay of various physical parameters such as doping at electron and hole pockets as well as non-zero nesting between the electron and hole pocket. We find that in the absence of magnetic order, the currents due to hole pocket and electron pocket add up ordinarily. However, in the presence of magnetic ordering, the two currents take part in characteristic interference effect to modify the resultant current significantly. This interference effect manifests itself in the non-monotonous and oscillatory nature of a beam splitter current. We investigate in detail this non-monotonicity with the chemical potential as well as nesting vectror | q | . We also investigate the evolution of density of states with system parameters and correlate it with the beam-splitter current. Furthermore, we enumerate the relevant parameter space where the efficiency of such a beam splitter setup is enhanced. Our finding can be useful in experimental determination or verification of a coexistence phase in iron-pnictide superconductors and has potential applications in realizing quantum gates or switches. [ABSTRACT FROM AUTHOR]

In our current era, numerical simulations have become indispensable theoretical and experimental tools for use in daily research activities, particularly in the materials science fields. However, the installation processes for such simulations frequently become problematic because they depend strongly on the device environment, and troubleshooting those processes is a challenging task for beginners. To minimize such difficulties, we created MateriApps LIVE! and MateriApps Installer, which can solve most of the related issues. Specifically, MateriApps LIVE! offers a virtual environment in which users can quickly try out computational materials science simulations on a personal computer while MateriApps Installer provides a comprehensive set of shell scripts for use when installing software on Unix, Linux, macOS, and supercomputer systems. Herein, we provide detailed descriptions of MateriApps LIVE! and MateriApps Installer together with illustrative examples of their use.

Results about entanglement (or modular) Hamiltonians of quantum many‐body systems in field theory and statistical mechanics models, and recent applications in the context of quantum information and quantum simulation, are reviewed. In the first part of the review, what is known about entanglement Hamiltonians of ground states (vacua) in quantum field theory is summarized, based on the Bisognano–Wichmann theorem and its extension to conformal field theory. This is complemented with a more rigorous mathematical discussion of the Bisognano–Wichmann theorem, within the framework of Tomita–Takesaki theorem of modular groups. The second part of the review is devoted to lattice models. There, exactly soluble cases are first considered and then the discussion is extended to non‐integrable models, whose entanglement Hamiltonian is often well captured by the lattice version of the Bisognano–Wichmann theorem. In the last part of the review, recently developed applications in quantum information processing that rely upon the specific properties of entanglement Hamiltonians in many‐body systems are summarized. These include protocols to measure entanglement spectra, and schemes to perform state tomography. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We studied a multi-orbital Hubbard model at half-filling for two and three orbitals per site on a two-site cluster via full exact diagonalization, in a wide range for the onsite repulsion U, from weak to strong coupling, and multiple ratios of the Hund coupling J H to U. The hopping matrix elements among the orbitals were also varied extensively. At intermediate and large U, we mapped the results into a Heisenberg model. For two orbitals per site, the mapping is into a S = 1 Heisenberg model where by symmetry both nearest-neighbor (S i â‹... S j ) and ( S i â‹... S j ) 2 are allowed, with respective couplings J 1 and J 2. For the case of three orbitals per site, the mapping is into a S = 3/2 Heisenberg model with (S i â‹... S j ), ( S i â‹... S j ) 2 , and ( S i â‹... S j ) 3 terms, and respective couplings J 1, J 2, and J 3. The strength of these coupling constants in the Heisenberg models depend on the U, J H, and hopping amplitudes of the underlying Hubbard model. Our study provides a first crude estimate to establish bounds on how large the ratios J 2/ J 1 and J 3/ J 1 can be. We show that those ratios appear rather limited and, as a qualitative guidance, we conclude that J 2/ J 1 is less than 0.4 and J 3/ J 1 is less than 0.2, establishing bounds on effective models for strongly correlated Hubbard systems. Moreover, the intermediate Hubbard U regime was found to be the most promising to enhance J 2/ J 1 and J 3/ J 1. [ABSTRACT FROM AUTHOR]

The formation of the excitation spectra of the ground state for Kondo insulators like YbB12, CeFe2Al10 has been studied and analyzed in terms of correspondence between cooperative and local effects. Experimental results concerning different types of substitutions for the rare earth and d-metal sublattices are discussed on the basis of model calculations. It is shown how the transformation from Kondo insulator to heavy fermions occurs in the f-electron excitation spectra of CeFe2Al10. [ABSTRACT FROM AUTHOR]

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models (Chen et al 2020 Phys. Rev. B 101 165123), is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

We present the results of measuring the dynamic magnetic susceptibility and surface impedance of a unique layered organic superconductor κ-(BEDT-TTF)4Hg2.89Br8 (κ-HgBr). In this material, strong electronic correlations coexist with weak doping associated with lattice incommensurability. The superconducting properties of this material are studied by several methods: the temperature dependences of the resistance across the conducting layers, the dynamic magnetic susceptibility, and the surface impedance in the conducting planes are measured. The results of measuring the resistance and dynamic magnetic susceptibility at a frequency of 100 kHz demonstrated the presence of a superconducting state at temperatures below Tc = 3.1 K. The results of measuring the temperature dependence of the surface impedance Z(T) = R(T) + iX(T) of several samples at a frequency of 28 GHz in the temperature range from 0.5 K to 50 K turned out to be unusual. In the studied samples at T < 3 K, a sharp change in Z(T) is not observed, and some samples even demonstrate weak "dielectricization" at low temperatures. [ABSTRACT FROM AUTHOR]

[Display omitted] Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems. [ABSTRACT FROM AUTHOR]

The problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region is considered, using the available strong‐coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP), the goal is to find classes of approximants that give well‐converged results already for low perturbative truncation orders. First, it is shown that the standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so‐called maximum‐entropy (MaxEnt) extrapolation method. However, it is shown that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is, thus, not practical for the CEP in this case. Instead, order‐dependent‐mapping extrapolation (ODME) as a simple, practical, and general method for the CEP is proposed. It is found that the ODME approximants for the ground‐state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties. [ABSTRACT FROM AUTHOR]

Entanglement is considered a fundamental ingredient for quantum technologies, while condensed matter systems are among the good candidates for the development of practical devices for quantum processing. For bipartite pure states the von Neumann entropy is a proper measure of entanglement, while the linear entropy, associated to the mixedness of the reduced density matrices, is a simpler quantity to be obtained and is considered to be qualitatively equivalent to the von Neumann. Here we investigate both linear and von Neumann entropies for quantifying entanglement in homogeneous, superlattice and disordered Hubbard chains. We find that for low densities systems (n ≲ 0. 6) the linear entropy fails in reproducing the qualitative behavior of the von Neumann entropy. This then may lead to incorrect predictions (i) of maximum and minimum entanglement states and (ii) of quantum phase transitions. • We compare linear and von Neumann entropies in the fermionic Hubbard model. • For small densities we find that the linear entropy fails to predict the qualitative behavior of entanglement. • We find that this failure of the linear entropy may lead to incorrect predictions of quantum phase transitions. • We exemplify our results in superlattices and disordered nanostructures. [ABSTRACT FROM AUTHOR]

In this paper, the crystal field parameters (CFPs) have been calculated in the framework of the density functional theory using a novel theoretical approach proposed by Pavel Novák et al. and extracting the WANNIER functions from the Bloch eigenstates for the CeCl3 compound. Then, the calculated CFPs have been used in an effective atomic-like Hamiltonian, including the crystal field, 4f-4f correlation and spin-orbit coupling, and the splitted energy levels of Ce3+ ion by crystal field have been derived by diagonalization of the Hamiltonian. A hybridization parameter, , has been used to improve the results. The results are found to be in agreement with the experimental data

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis. [ABSTRACT FROM AUTHOR]

Ab-initio density functional theory (DFT)＋ U has been used to study the spin-resolved electronic band structure and the partial density of states of the multiferroic XY-antiferromagnetic Ba 2 CoGe 2 O 7. Using the constrained random-phase approximation (cRPA) method, the value of Hubbard U and Hund's coupling J H has been determined and plugged into the further dynamical mean field theory (DMFT) calculations. The strong metal-ligand hybridization between Co-3 d and O-2 p orbitals in the CoO 4 tetrahedron has been demonstrated via DFT and DFT＋DMFT calculations. The calculated indirect band gap in the antiferromagnetic state without and with U (= 5 eV) correction is found to be 0.67 and 2.71 eV, respectively. The highest calculated ordered magnetic moment of 2.7 μ B /Co 2 + is close to the reported experimental value. The presented DFT calculations based on the different orbital models brings the underlying strong electronic correlation in the Ba 2 CoGe 2 O 7. [ABSTRACT FROM AUTHOR]

To probe the energy of dielectric coupling between the dipole chains and the quasipolarons based on extension of the polaron concept, dielectric and magnetic properties of antiferromagnetic insulators, namely Ca _4-x Cu _x Ti _4 O _12 (x = 3, 2 and 1), are investigated at different temperatures. The energy is estimated larger than 56 meV of the dipole interaction energy, but smaller than 88 meV of the dipole-chain thermal activation energy which is for the Dissado-Hill type dielectric relaxation. In particular, the quasipolaron ingredient is at least 28 meV of the total superexchange interaction which bond one singe titanium ion of the dipole chain with four quasipolarons. Then, the energy of the coupling is in the range from 84 meV to 88 meV. The experimental observation, suggests the dielectric coupling may provide an approach to obtain large permittivity in strongly-correlating systems of antiferromagnetic insulators.

The dimer Mott insulator λ-(BEDT-STF)2GaCl4 undergoes no magnetic order down to the lowest temperatures, suggesting the formation of a novel quantum disordered state. Our frequency and temperature-dependent investigations of the dielectric response reveal a relaxor-like behavior below T≈100 K for all three axes, similar to other spin liquid candidates. Optical measurement of the charge-sensitive vibrational mode ν27(b1u) identifies a charge disproportionation Δρ≈0.04e on the dimer that exists up to room temperature and originates from inequivalent molecules in the weakly coupled dimers. The linewidth of the charge sensitive mode is broader than that of typical organic conductors, supporting the existence of a disordered electronic state.

We present an introduction to Landau's Theory of Fermi Liquids. We seek to highlight the paradigms established by Lev Landau in the 1950s, which influence the development of current research areas. In turn, we argue that it is possible to teach this theory in physics undergraduate courses, having a positive impact on the knowledge building of professionals specialized in areas such as Solid State and Strongly Correlated Electrons. The presentation is constructive, self-contained and aimed at Physics undergraduate and graduate students. As an example, we study wave propagation in a simplified two-dimensional Fermi liquid model. The output is related with one of Landau's best known results, the �zero sound� excitation. [ABSTRACT FROM AUTHOR]

The structural and magnetic properties of the overexpanded quaternary K 0.25 Rb 0.25 Cs 2.5 C 60 fulleride are investigated. Rietveld analysis of the high-resolution synchrotron X-ray powder diffraction data shows that K 0.25 Rb 0.25 Cs 2.5 C 60 adopts a cubic structure with face-centered (fcc) symmetry. Magnetization measurements at ambient pressure reveal that the material is a superconductor with a transition temperature, T c , of 29.4 K. Temperature dependence of the magnetic susceptibility does not show a simple temperature-independent Pauli susceptibility term – instead, it shows a cusp at a certain temperature implying an insulator-to-metal crossover on cooling. Complementary high-pressure magnetization measurements to a pressure of 10.2 kbar show a non-monotonic response of T c with a dome-shaped scaling with pressure and a maximum value of 32.4 K at 3.9 kbar. The experimental results are consistent with quaternary K 0.25 Rb 0.25 Cs 2.5 C 60 following the established unconventional behavior of overexpanded fullerides. However, our results also unveil well-defined detrimental cation specific effects on the electronic properties associated with the introduction of increased disorder in the tetrahedral interstices of the fcc fulleride structure. • The tetrahedrally-residing cations in alkali fullerides influence the molecular electronic properties via the size mismatch. [ABSTRACT FROM AUTHOR]