Numerical Diagonalization Method Research Articles

Synthesis, molecular and crystalline architectures, and properties of a mononuclear complex [Co II (benzidine) 2 (NCS) 2 (OH 2 ) 2

One mononuclear cobalt(II) compound of the type [Co(bnzd)2(NCS)2(OH2)2] (1) (bnzd = benzidine) has been isolated through a single-pot reaction of the molecular building components in MeOH–H2O solvent mixture at room temperature and characterized by physico-chemical and spectroscopic methods. The crystal structure of complex 1 has an octahedral geometry with trans, trans, trans orientations in the order (Na,Na), (Nt,Nt), (Ow,Ow) [Na = N(amine), Nt = N(thiocyanate) and Ow = O(water)]. In crystalline state, individual units of 1 are associated by weak cooperative O–H...N, O–H...S and N–H...S hydrogen bonds resulting in a 3D network structure. The compound is redox active and shows luminescence in MeOH solution. Thermal decomposition pattern of 1 reveals the presence of two coordinated water molecules. Variable-temperature magnetic susceptibility measurement shows significant orbital contribution and numerical matrix diagonalization method gives the best fit parameters: α = A*k = 1.43; λ = −130 cm − 1; Δ = − 864 cm − 1; TIP = 0.000975; R = 1.19 × 10 − 4. Mononuclear compound [Co(benzidine)2(NCS)2(OH2)2] (1) was isolated and characterized. Cobalt(II) center adopts an octahedral geometry and individual units of 1 are associated by weak O–H…N/S and N–H…S hydrogen bonds resulting in a 3D network structure. Complex 1 is electroactive and shows luminescence property. Variable-temperature magnetic property shows significant orbital contribution.

Critical behavior of the fidelity susceptibility for the [formula omitted] transverse-field Ising model

The overlap (inner product) between the ground-state eigenvectors with proximate interaction parameters, the so-called fidelity, plays a significant role in the quantum-information theory. In this paper, the critical behavior of the fidelity susceptibility is investigated for a two-dimensional transverse-field (quantum) Ising model by means of the numerical diagonalization method. In order to treat a variety of system sizes N=12,14,…,32, we adopt the screw-boundary condition. Finite-size artifacts (scaling corrections) of the fidelity susceptibility appear to be suppressed, as compared to those of the Binder parameter. As a result, we estimate the fidelity susceptibility critical exponent as αF=0.715(20).

Long-Range Order of the Three-Sublattice Structure in the S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice

We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \simle J_2/J_1 \le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.

Antiferromagnetic Exchange Interaction between Electrons on Degenerate LUMOs in Benzene Dianion

We discuss the ground state of Benzene dianion (Bz$^{2-}$) on the basis of the numerical diagonalization method of an effective model of $\pi$ orbitals. It is found that the ground state can be the spin singlet state, and the exchange coupling between LUMOs can be antiferromagnetic.

Thermal entanglement witness for interacting itinerant fermion systems

The Hubbard model describes interacting itinerant fermion systems and is the simplest model capable of describing the essential physics of strongly correlated electron systems. In this model, both spin correlations and charge correlations are important for the entanglement, thus the magnetic susceptibility is not an appropriate thermal entanglement witness. The specific heat reflects spin correlations and charge correlations. We obtain a relation that permits the specific heat to be used directly as a thermal entanglement witness. We calculate, away from half filling, the entanglement critical temperature ${T}_{E}$, below which entanglement is detected, for small linear clusters and the hypercubic lattice in the limit of infinite dimensions by using the exact numerical diagonalization method and the dynamical mean-field theory, respectively. We find, in both cases, that ${T}_{E}$ increases with increasing strength of the on-site Coulomb repulsion $U$.

Deconfined-critical behavior of the VBS- and nematic-order parameters for the spatially anisotropic [formula omitted]-spin model

The phase transition between the valence-bond-solid (VBS) and nematic phases, the so-called deconfined criticality, was investigated for the quantum S=1-spin model on the spatially anisotropic triangular lattice with the biquadratic interaction by means of the numerical diagonalization method. We calculated both VBS- and nematic-order parameters, aiming to clarify the nature of this transition from complementary viewpoints. Simulating the clusters with N≤20 spins, we estimate the correlation-length critical exponent as ν=0.95(14). We also calculated Fisher’s exponent (anomalous dimension) for each order parameter.

A Consistent Description of Magnetic Properties of the Triangulated-Kagome System Cu9X2(cpa)6·nH2O

A consistent description of the behaviors of both the magnetic susceptibility and of the 1/3-plateau like magnetization under a magnetic field in the triangulated-kagome compound Cu 9 X 2 (cpa) 6 · n H 2 O (X = F, Cl, Br; cpa = the anion of 2-carboxypentonic acid) is given by the Heisenberg model with the antiferromagnetic next-nearest-neighbor interaction, in addition to the two types of antiferromagnetic nearest-neighbor interactions in previous studies. This description is provided by the method of numerical diagonalization. The newly introduced interaction derives the quantum phase transition from the quantum-disordered-state to the ferrimagnetic one. The stability of the magnetization plateaus is complemented using the perturbation theory.

Spin frustration, charge ordering, and enhanced antiferromagnetism in TMTTF2SbF6

We theoretically investigate the effects of charge order and spin frustration on the spin ordering in TMTTF salts. Using first-principles band calculations, we find that a diagonal inter-chain transfer integral tq1, which causes spin frustration between the inter-chain dimers in the dimer-Mott insulating state, strongly depends on the choice of anion. Within the numerical Lanczos exact diagonalization method, we show that the ferroelectric charge order changes the role of tq1 from the spin frustration to the enhancement of the two-dimensionality in spin sector. The results indicate that tq1 assists the cooperative behavior between charge order and antiferromagnetic state observed in TMTTF2SbF6.

Néel-VBS phase boundary of the extendedJ1-J2model with biquadratic interaction

The ${J}_{1}$-${J}_{2}$ model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking advantage of the extended parameter space, we survey the phase boundary separating the N\'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with $N\ensuremath{\leqslant}36$ spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is $\ensuremath{\nu}=1.1(3)$. In order to elucidate a nonlocal character of criticality, we evaluated the Roomany-Wyld $\ensuremath{\beta}$ function around the critical point.

Magnetization ramp of the kagome lattice antiferromagnet

The magnetization process of the Heisenberg antiferromagnet on the kagome lattice is studied by numerical-diagonalization method. Though the magnetization plateau was considered to appear at the one-third of the magnetization saturation, recent reexamination of the magnetization process of the same model from another viewpoint of the field-derivative of the magnetization in finite-size data from the numerical-diagonalization calculation up to 36 sites suggests that the behavior at around one-third height of the saturation is clearly different from typical magnetization plateaux, which we should call the magnetiztaion ramp. The present study reports our new numerical-diagonalization result up to 39 sites, which reveals well the characteristics of the magnetization ramp. The behavior of the kagome lattice antiferromagnet is compared with the typical magnetization plateux of the Heisenberg antiferromagnet on the triangular lattice.

Numerical exact diagonalization study of triangulated kagome Heisenberg spin system

The thermodynamic properties and the magnetization under magnetic field at zero temperature of the spin-1/2 Heisenberg model on triangulated kagome lattice, which composed of two sublattices, are investigated by numerical exact diagonalization method for 18 and up to 27 spin clusters, respectively. The temperature dependence of magnetic susceptibility may be reproduced qualitatively with the weak ferromagnetic intersublattice nearest neighbor exchange coupling constant JAB as proposed by previous studies, although it is quantitatively insufficient in comparison with the experimental result. The magnetization under magnetic field shows the 5/9 plateau for every examined values of JAB, but 1/3 plateau, visible in the experiment, may be reproduced only for not so weak antiferromagnetic case of JAB. This discrepancy for JAB in those two qualities has also been recognized in previous studies on classical spin models and is not still resolved even for the present quantum spin system.

Excited-state absorptions of an exciton confined in a quantum dot

The optical absorptions of an exciton with the higher excited states in a disc-like quantum dot are investigated. Calculations are made by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. With typical semiconducting GaAs based materials, the linear, third-order nonlinear, total optical absorption coefficients and refractive index changes have been calculated for the s–p, p–d, and d–f transitions. The results show that as the angular momentum quantum number of transitions increases, the absorption peaks shift towards lower energies and the absorption intensities increase.

A study of nonlinear optical properties of a negative donor quantum dot

In this paper, we studied the nonlinear optical properties of a negative donor center ( D −) in a disk-like quantum dot (QD) with a Gaussian confining potential. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. A detailed investigation of the linear, third-order nonlinear, total optical absorptions and refractive index changes has been carried out for the D − QD and the D 0 QD. The linear, third-order nonlinear, total optical absorptions and refractive indices have been examined for a double-electron QD with and without impurity. Our results show that the optical absorption coefficients and refractive indices in a disk-like QD are much larger than their values for quantum wells and spherical QDs and the nonlinear optical properties of QDs are strongly affected not only with the confinement barrier height, dot radius, the number of electrons but also the electron-impurity interaction.

Electron and hole energy levels in InAs/GaAs quantum dots: Size and magnetic field effects

We present a systematic study on the influence of strain, size, and magnetic field on the electronic properties of InAs/GaAs quantum dots. Using a 40-band k.p model, we have calculated the band diagram of strained InAs, and extract the band parameters which are useful for the electronic properties of InAs/GaAs quantum dots. Then, using an exact numerical diagonalization method on Fourier–Bessel function basis over a large cylinder domain, we calculated numerically the electron and hole eigenenergies and associated wave functions. We considered thereafter the effect of an external applied magnetic field, strain and quantum dot size variation on the charge carrier energy levels. It is clearly found that the strain strongly modifies the quantum dot potential profile, leading to a different electron and hole energy distribution. Our results revealed also that the electron and hole energy spectra change significantly when varying the quantum dot size as well as the magnetic field. Given this striking nanostructure size and magnetic field energy dependent property, these systems provide the opportunity to control and tune their optical and electronic properties through these parameters.

Nonlinear optical properties of a D− system in a spherical quantum dot

The nonlinear optical properties of a D− system confined in a spherical quantum dot represented by a Gaussian confining potential are studied. The great advantage of our methodology is that the model potential possesses the finite height and range. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. We calculate the linear, third-order nonlinear and total optical absorption coefficients under the density matrix formalism. Numerical results for GaAs−Ga1−xAlxAs QDs are presented. Our results show that the optical absorption coefficients in a spherical QD are much larger than their values for GaAs quantum wells. It is found that optical absorptions are strongly affected not only the confinement barrier height, dot radius, the electron–impurity interaction but also the position of the impurity.

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mott-insulator (MI), density wave (DW) and modulated superfluid (MS) phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.

Magnetization Process of Kagome-Lattice Heisenberg Antiferromagnet

The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".

Criticality of the [formula omitted]-dimensional [formula omitted] transverse-field Ising model with extended interactions: Suppression of corrections to scaling

The criticality of the ( 2 + 1 ) -dimensional S = 1 transverse-field Ising model is investigated with the numerical diagonalization method. The scaling behavior is improved by tuning the coupling-constant parameters; the S = 1 spin model allows us to incorporate a variety of interactions such as the single-ion anisotropy and the biquadratic interactions. Simulating the clusters with N = 6 , 8 , … , 20 spins, we estimate the critical indices as 1 / ν = 1.586 ( 6 ) and η = 0.034 ( 4 ) .

Optimized structure and thermodynamic properties of atomic clusters in the framework of the extended Hubbard model

By using a numerical exact diagonalization method, the properties of atomic clusters with atom number N=5 and N=6 are investigated in the framework of the extended Hubbard model. The optimized structure and the corresponding total spin S are obtained both as a function of Hubbard onsite interaction U, nearest-neighbor Coulomb repulsion V and filling number of electrons. Results show that with V increasing, the optimized structure of cluster turns into a chain or star-like structure with fewer bonds. The thermodynamic properties are also analyzed based on the distribution of energy levels of cluster with an optimized structure.

Negative impurity magnetic susceptibility and heat capacity in a Kondo model with narrow peaks in the local density of electron states

Temperature dependences of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be negative. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it.