Complete Diagonalization Research Articles

Intraband Exciton Transitions in Photosynthetic Complexes Revealed by Novel Five-Wave-Mixing Spectroscopy.

We calculate the χ(4) optical response of an oriented photosystem II reaction center of purple bacteria described by the Frenkel exciton model using nonlinear exciton equations (NEE). This approach treats each chromophore as an anharmonic oscillator and provides an intuitive quasiparticle picture of nonlinear spectroscopic signals of interacting excitons. It provides a computationally powerful description of nonlinear spectroscopic signals that avoids complete diagonalization of the total Hamiltonian. Expressions for the second- and the fourth-order nonlinear signals are derived. The NEE have been successfully employed in the past to describe even-order-wave-mixing. Here, we extend them to aggregates with broken inversion symmetries. Even-order susceptibilities require the introduction of permanent dipoles, which allow to directly probe low-frequency intraband transitions of excitons.

Theoretical studies and structural analysis of the Nd3+ centers with trigonal symmetry in congruent lithium niobate single crystals

In this paper, the superposition model (SM) and complete diagonalization procedure of energy matrix (CDM method) were used for a few selected Nd3+ (4f3) paramagnetic centers with trigonal symmetry in congruent lithium niobate (LN, LiNbO3) single crystals. Additionally, the g-shift method was applied to these systems. In general, the calculated g-factors (parallel and perpendicular) match the measured values very well. The displacements of the Nd3+ ions calculated by g-shift method are also fit very well to the experimental values. A detailed structural analysis of paramagnetic Nd3+ centers with trigonal symmetry in congruent LN single crystals was also performed. The charge compensation mechanism and its role in establishing Nd3+ centers in congruent LN are also debated.

Theoretical and Structural Study of Axial Symmetry Ce3+ Centers in the BaWO4 Single Crystal Doped with Cerium and Codoped with Sodium Ions.

The spin–Hamiltonian parameters g–factors ( and ) of the Ce3+ paramagnetic centers in BaWO4: Ce and BaWO4: Ce, Na single crystals with axial symmetry are investigated using the superposition model (SPM) via complete diagonalization procedure of energy matrix (CDM method). The calculated g–factors are in reasonable agreement with the experimental values. The fitted intrinsic parameters are comparable with data from other publications for rare-earth paramagnetic centers in a similar environment. The angular distortions of the cerium dodecahedron [CeO8] are also studied. Structural analysis of paramagnetic centers with axial symmetry through the postulated cerium barium tetrahedron [CeBa4] connected via oxygens bridges was carried out. The mechanism of the charge compensation and the role of the second dopant (Na+) is also discussed.

Quintic-scaling rank-reduced coupled cluster theory with single and double excitations.

We consider the rank-reduced coupled-cluster theory with single and double (RR-CCSD) excitations introduced recently [Parrish et al., J. Chem. Phys. 150, 164118 (2019)]. The main feature of this method is the decomposed form of doubly excited amplitudes, which are expanded in the basis of largest magnitude eigenvectors of MP2 or MP3 amplitudes. This approach enables a substantial compression of amplitudes with only minor loss of accuracy. However, the formal scaling of the computational costs with the system size (N) is unaffected in comparison with the conventional CCSD theory (∝N6) due to the presence of some terms quadratic in amplitudes, which do not naturally factorize to a simpler form even within the rank-reduced framework. We show how to solve this problem, exploiting the fact that their effective rank increases only linearly with the system size. We provide a systematic way to approximate the problematic terms using the singular value decomposition and reduce the scaling of the RR-CCSD iterations down to the level of N5. This is combined with an iterative method of finding dominant eigenpairs of MP2 or MP3 amplitudes, which eliminates the necessity to perform the complete diagonalization, making the cost of this step proportional to the fifth power of the system size, as well. Next, we consider the evaluation of perturbative corrections to CCSD energies resulting from triply excited configurations. The triply excited amplitudes present in the CCSD(T) method are decomposed to the Tucker-3 format using the higher-order orthogonal iteration procedure. This enables us to compute the energy correction due to triple excitations non-iteratively with N6 cost. The accuracy of the resulting rank-reduced CCSD(T) method is studied for both total and relative correlation energies of a diverse set of molecules. Accuracy levels better than 99.9% can be achieved with a substantial reduction of the computational costs. Concerning the computational timings, the break-even point between the rank-reduced and conventional CCSD implementations occurs for systems with about 30-40 active electrons.

Theoretical Investigation of the EPR G-Factor for the Axial Symmetry Ce3+ Center in the BaWO4 Single Crystal

The parameters g-factor (g|| and g⊥) together with the local structure of the Ce3+ center in BaWO4 single crystal (scheelite structure crystals) were theoretically investigated using a complete diagonalization procedure of energy matrix (CDM method). The intrinsic parameters were calculated. It is shown that the experimental and the calculated values of the g-factors are in good agreement. The angular distortion has also been calculated. It was found that the polar angles of the impurity–ligand bonding are smaller than in BaWO4 single crystal (Δθ≈1.0° ) . The validity of the results and the changing in the local environment of the impurity–cerium ion is also discussed.

Fine structure of energy levels and electron paramagnetic resonance parameters of Ni2+ doped in CsCdCl3

Complete diagonalization method (CDM) and high-order perturbation method (PTM) with forth-order formulae have been used to explain the optical spectra and ground term 3A2g electron paramagnetic resonance (EPR) parameters g//,g⊥ and zero-field splitting (ZFS) parameter D of Ni2+-doped CsCdCl3 within the framework of molecular orbital (MO) scheme, the calculated results are in good agreement with the experimental data. The trigonal parametersv and v′, Reach parameters B and C and the local defect structure are determined. The effect of vibronic interaction on optical spectra of 3T2g and 3A2g transition has been discussed with a1g and eg vibronic models, and the Huang–Phys parameters and vibronic coupling constant are evaluated.

Relationship between the gyromagnetic anisotropy and tetragonal distortion for d 1 ions in octahedral clusters

The gyromagnetic (g) factors of vanadium (IV) (V4+) tetragonally-distorted octahedra in ‘bulk’ (where g-anisotropy Δg = g //−g ⊥>0) and surface (where Δg < 0) of metal oxides are studied from complete diagonalization method and perturbation theory method. The calculated g factors for small and large tetragonal distortions agree with the observed values of V4+ in ‘bulk’ and surface of metal oxides, respectively. So the sign of Δg for d 1 octahedra depend upon the magnitude of tetragonal distortion rather than the ground state as in the complementary d 9 octahedral clusters. Similar case can also be found for d 9 ions in tetragonally-distorted tetrahedral clusters.

Investigation of the Electronic Structure and Optical, EPR, and ODMR Spectroscopic Properties for 171Yb3+-Doped Y2SiO5 Crystal: A Combined Theoretical Approach.

Various spectroscopic properties of Yb3+-doped Y2SiO5 crystal have been extensively investigated due to its promising application in quantum information processing. However, the local structure, electronic structure of Yb3+:Y2SiO5 crystal, and its optical and magnetic properties have not been comprehensively studied from a theoretical viewpoint. In this work, the geometric and electronic structures of Yb3+ that replaces two crystallographic Y3+ sites in the Y2SiO5 crystal are first obtained by the method of density functional theory (DFT). Then, the optical, electron paramagnetic resonance (EPR), and optically detected magnetic resonance (ODMR) spectra for 171Yb3+ (nuclear spin I = 1/2) at such two sites are simultaneously calculated in the framework of the complete diagonalization (of energy) matrix (CDM) based on the optimized local structure around 171Yb3+ ion by DFT. The various calculated spectroscopic properties by such combined theoretical approach are consistent with the experimental ones, which demonstrates that CDM is effective and particularly suitable for calculating hyperfine A-tensors under zero, low, and intermediate magnetic field. More importantly, based on the obtained accurate hyperfine structure of 171Yb3+ in Y2SiO5 crystal, the possible "clock transitions", which can enhance the optical coherence time, can be assigned or predicted by the present approach. This study successfully explains the spectroscopic properties of 171Yb3+-doped Y2SiO5 and provides a feasible method to design and search for practical rare-earth-doped quantum information materials for the community.

Enhancement of magnetization plateaus in low-dimensional spin systems

We study the low-energy properties and, in particular, the magnetization process of a spin-1/2 Heisenberg $J_1-J_2$ sawtooth and frustrated chain (also known as zig-zag ladder) with a spatially anisotropic $g$-factor. We treat the problem both analytically and numerically while keeping the $J_2/J_1$ ratio generic. Numerically, we use complete and Lanczos diagonalization as well as the infinite time-evolving block decimation (iTEBD) method. Analytically we employ (non-)Abelian bosonization. Additionally for the sawtooth chain, we provide an analytical description in terms of flat bands and localized magnons. By considering a specific pattern for the $g$-factor anisotropy for both models, we show that a small anisotropy significantly enhances a magnetization plateau at half saturation. For the magnetization of the frustrated chain, we show the destruction of the $1/3$ of the full saturation plateau in favor of the creation of a plateau at half-saturation. For large anisotropies, the existence of an additional plateau at zero magnetization is possible. Here and at higher magnetic fields, the system is locked in the half-saturation plateau, never reaching full saturation.

Investigations of crystal-field energy levels and microscopic spin-Hamiltonian parameters of Mn4+ ions in pyrochlore hosts Y2Ti2O7 and Y2Sn2O7

We investigate the crystal-field energy levels and the microscopic origin of spin-Hamiltonian parameters (SHPs), i.e. g-factors and zero-field splitting parameter D, for the ground state 4A2g(4F) of Mn4+ impurity ions at trigonal sites in host pyrochlores, Y2Ti2O7 and Y2Sn2O7. The total Hamiltonian includes the electrostatic and crystal-field (CF) Hamiltonians, and the magnetic interactions, i.e. spin-orbit, spin-spin, spin-other-orbit, and orbit-orbit couplings. The calculations are performed under the complete diagonalization method and microscopic spin-Hamiltonian (CDM/MSH) program. The calculated CF levels agree reasonably well with the observed energy levels for Mn4+ ions in these compounds. The SHPs are evaluated with the CDM/MSH wave functions as well as by a perturbation loop theory method (PLTM). The g-factors of Mn4+ in Y2Ti2O7 and Y2Sn2O7 using PLTM are close to those evaluated by CDM, while the PLTM value of D shows appreciable difference with the CDM value. This evidences that the g-factors depend predominately on the lower states, while the higher energy states significantly affect the D value. The contributions of spin-spin, spin-other-orbit, and orbit-orbit couplings to the CF energy levels and the SHPs are discussed.

Maximum advantage of quantum illumination

Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimension of the states grow large. In this article, we analyze quantum illumination as a quantum channel discrimination protocol and circumvent these issues by using the normalized Hilbert-Schmidt inner product as a measure of distinguishability. Using this measure, we show that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state.

United calculation of the optical and EPR spectral data for Co2+-doped CdS crystal

This article reports a united calculation of the optical band positions and EPR parameters (g factors g//, g⊥ and zero-field splitting D) for Co2+ ion at the trigonal tetrahedral Cd2+ site of CdS crystal by using the complete diagonalization (of energy matrix) method built on the cluster approach. In the approach, the one-electron basis functions are the molecular orbitals composed of the d orbitals of central dn ion and p orbitals of ligands (rather than only the pure d orbitals in the conventional crystal-field theory), and so the contributions from not only the spin-orbit parameter of dn ion, but also that of ligand ion are contained. The calculated results are in rational agreement with the twenty-two (nineteen optical band positions and three EPR parameters) observed spectral values found in the literature. The defect structure (particularly, the angular distortion) of the trigonal Co2+ center in CdS: Co2+ is also acquired by the calculation. The outcomes are discussed.

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrodinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. We analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4\pi$-periodic supercurrent.

Exploration of the structural and optical properties of a red-emitting phosphor K2TiF6:Mn4+**Project supported by the National Natural Science Foundation of China (Grant No. 11574220), Fundamental Research Funds for the Central Universities, China (Grant No. SWU118055), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), China.

The exploration of the appropriate red phosphor with good luminescence properties is an important issue in the development of current white light-emitting diode (WLED) devices. Transition metal Mn-doped compounds are fascinating luminescent materials. Herein, we performed a systematic theoretical study of the microstructure and optical properties of K2TiF6:Mn4+ using the CALYPSO structure search method in combination with first-principles calculations. We uncovered a novel structure of K2TiF6:Mn4+ with space group P-3m1 symmetry, where the impurity Mn4+ ions are accurately located at the center of the MnF6 octahedra. Based on our developed complete energy matrix diagonalization (CEMD) method, we calculated transition lines for 2Eg → 4A2, 4A2 → 4T2, and 4A2 → 4T2 at 642, nm, 471 nm, and 352 nm, respectively, which are in good agreement with the available experimental data. More remarkably, we also found another transition (4A2 → 2T2) that lies at 380 nm, which should be a promising candidate for laser action.

Systematic analysis of the fine structure of energy levels and spin-Hamiltonian parameters of V3+ ion in corundum with dynamic Jahn-Teller effect

Systematic analysis of fine structure of the whole energy levels and spin-Hamiltonian parameters (zero-field splitting (ZFS) parameter D and g-factors g// and g⊥) for the ground state 3A2 (3T1) of V3+ ion in corundum are presented in detail with complete diagonalization method (CDM) of 45 × 45 energy matrix, in which the full configuration interactions are taken into account. The reduction of the splittings of excited electronic 3T2 (t2 ge) term with orbital triplet degenerate caused by spin-orbit (SO) and lower trigonal crystal field (CF) is studied by T2⊗e model dynamic Jahn-Teller theory, and Ham deduction factor, the Jahn-Teller energy EJT and Huang-Rhys factor S are estimated. The studies are performed within the strong-field scheme with molecular orbit (MO) approximation, in which the two SO coupling parameter model is used and the SO contributions from both the central 3d ion and ligands are taken in account. The calculated results are in good agreement with the experimental data, and the local structure of [VO6]9- cluster with C3 point group symmetry are determined quantitatively.

Investigations of the electron paramagnetic resonance parameters and defect structures for Cu2+ ions in BeO crystal with trigonally distorted tetrahedral symmetry

Abstract The electron paramagnetic resonance(EPR) parameters (g factors gi and hyperfine structure constants Ai, where i = x, z) for Cu2+ ions embedded in beryllium oxide (BeO) crystal at Be2+ sites with C3v local symmetry have been calculated by the complete diagonalization method (CDM) and high-order perturbation theory method (PTM). The calculated results from the two methods are in reasonable agreement with the observed data available. The defect structural data of the trigonal Cu2+ center in beryllium oxide are determined from the calculations and analyses. The calculated results show that the Be2+ ions are replaced by Cu2+ ions in BeO crystal and the ligands undergo outward movement.

Generator-coordinate reference states for spectra and 0νββ decay in the in-medium similarity renormalization group

We use a reference state based on symmetry-restored states from deformed mean-field or generator-coordinate-method (GCM) calculations in conjunction with the in-medium similarity-renormalization group (IMSRG) to compute spectra and matrix elements for neutrinoless double-beta ($0\nu\beta\beta$) decay. Because the decay involves ground states from two nuclei, we use evolved operators from the IMSRG in one nucleus in a subsequent GCM calculation in the other. We benchmark the resulting IMSRG+GCM method against complete shell-model diagonalization for both the energies of low-lying states in $^{48}$Ca and $^{48}$Ti and the $0\nu\beta\beta$ matrix element for the decay of $^{48}$Ca, all in a single valence shell. Our approach produces better spectra than either the IMSRG with a spherical-mean-field reference or GCM calculations with unevolved operators. For the $0\nu\beta\beta$ matrix element the improvement is slight, but we expect more significant effects in full ab-initio calculations.

Determination of the g-factors measured by EPR based on theoretical crystal field and superposition model analyses for lanthanide-based magnetically concentrated crystals – case study: double tungstates and molybdates

ABSTRACTThe methods developed for theoretical determination of g-factors measured by electron paramagnetic resonance (EPR) for single transition ions are extended to lanthanide-based magnetically concentrated crystals. The crystal field (CF) and superposition model (SPM) analyses are employed for optoelectronic materials: double tungstates and molybdates. Using the crystallographic data for Nd3+ ions in RbNd(WO4)2 and Yb3+ ions in KYb(MoO4)2 as input for SPM modelling, the CF parameters (CFPs) are predicted for the respective ions. The matrix for g tensor is calculated by the complete diagonalisation method. By matching three principal g values (gxx, gyy, gzz) to those measured by EPR, three adjustable SPM intrinsic parameters:, and are obtained. The reliability of the related CFPs is verified by comparative analysis of available data. The results demonstrate that the methods suitable for single lanthanide ions in crystal can be successfully applied to magnetically concentrated systems. The predicted g tensor anisotropy enables consideration of EPR linewidths arising from dipolar broadening in ALn(MO4)2 (A = alkali ions, Ln = lanthanide ions, M = W or Mo) systems based on the moment method, which requires accurate g-factors. The model parameters determined here may be utilised for SPM/CFP calculations for Nd3+ and Yb3+ ions in single-molecule magnets and single-ion magnets.

Investigations of the optical and EPR spectral data for the trigonal Cr3+ center in ZnGa2O4: Cr3+ crystal with a unified method-complete diagonalization of energy matrix

The optical and EPR spectral data of the trigonal Cr3+ centers in ZnGa2O4: Cr3+ crystal are unifiedly calculated by applying the complete diagonalization of energy matrix method resting on the two-spin-orbit-parameter model, where the one-electron basis functions are the molecular orbitals and the contributions from both the spin-orbit parameters of dn ion and ligand ion are included. Thus, the Racah parameters B, C, two spin-orbit parameters and two orbit reduction factors can be evaluated from a adjustable parameter, the covalence factor, and so only three adjustable parameters are used in the calculation. The ten calculated spectral data (seven optical band positions and three EPR parameters, g factors g//, g⊥ and zero-field splitting D) are rationally consistent with the experimental values. The defect structure of the trigonal Cr3+ center is also given. These outcomes are discussed.

Unified research of the EPR and optical spectral data for Cr3+-doped Lu3Al5O12 crystal

In this article, we apply a complete diagonalization (of energy matrix) method to simultaneously calculate the spin-Hamiltonian (or EPR) parameters (g factors g//, g⊥ and zero-field splitting D) and optical band positions (or crystal field energy levels) of Cr3+-doped Lu3Al5O12 (LuAG) crystal. The method is based on the two-spin-orbit-parameter model where besides the effects of spin-orbit parameter of central dn ion in the common crystal-field theory, those of ligand ions are contained. The calculated results indicate that by using only three adjustable parameters, the eight observed spectroscopic data (three EPR data and five optical bands) are reasonably explained. This suggests that this diagonalization method is effective and applicable in the unified calculation of EPR and optical spectral data for d3 ions in crystals. The local lattice distortion caused by the Cr3+ impurity in LuAG crystal is also estimated. The outcomes are discussed.