Numerical Diagonalization Method Research Articles

Binding energies of an exciton in a Gaussian potential quantum dot

In this paper, an exciton trapped by a Gaussian confining potential quantum dot has been investigated. Calculations are made by using the method of numerical diagonalization of Hamiltonian in the effective-mass approximation. The dependences of binding energies of the ground state and the first excited state on the size of the confining potential and the strength of the magnetic field are analysed explicitly.

Tetrahedral magnetic cluster embedded in metallic matrix: electron-correlation effects

A tetrahedral magnetic cluster surrounded by metallic atoms is studied in the framework of the Hubbard model. The ground-state energy and the wave function are obtained exactly using the Lanczos numerical diagonalization method. The spin/spin correlation functions /spl gamma//sub ij/= <S I.oarr="" S="" i="" j="" middot="" spl="" sub="" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> and the total spin S are analyzed as a function of the ratio between the on-site Coulomb repulsion U and electronic hopping t.

Low-energy excitations in a one-dimensional orthogonal dimer model with the Dzyaloshinski-Moriya interaction

Effects of the Dzyaloshinski-Moriya (DM) interaction on low-energy excitations in a one-dimensional orthogonal-dimer model are studied by using the perturbation expansions and the numerical diagonalization method. In the absence of the DM interaction, the triplet excitations show two flat spectra with three-fold degeneracy, which are lebeled by magnetization M=0, ±1. These spectra split into two branches with M=0 and with M=±1 by swithing-on of the DM interaction and besides the curvature appears in the triplet excitations with M=±1 more strongly than those of M=0.

Binding Energies of Negatively Charged Donors in a GaussianPotential Quantum Dot

We investigate a negatively charged donor centre (D−) trapped by aquantum dot, which is subjected to a Gaussian potential confinement.Calculations are carried out by using the method of numericaldiagonalization of Hamiltonian within the effective-mass approximation.The dependence of the ground state of the negatively charged donor onthe dot size and the potential depth is studied. The same calculationsperformed with the parabolic approximation of the Gaussian potentiallead to the results that are qualitatively and quantitatively different.

Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact 00u-type quantum plateau state, is also presented. The phase transition to the classical udu-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.

Energy spectrum analysis of donor-center quantum dots

Within the effective mass approximation, the energy spectra of the donor- center quantum dot system in Gaussian confining potential are calculated by using the method of numerical matrix diagonalization. The results show that the property of the ground and low-lying states of the quantum dot is rather sensitive to the size and the strength of confinement potential.

Magnetization Plateau of theS= 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation

The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑... and ↑↓↑↑↓↑... ) turned out to be robust against the period 3 exchange modulation which favors the ○-○ ↑○-○ ↑... phase up to a critical value of the modulation amplitude (○-○ = singlet dimer) resulting in the Z 2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓... configuration is stabilized for period 3 modulation with opposite sign. The transition between the ○-○↑ ○-○ ↑...-phase and Z 2 -broken phase is the Ising transition and that between the ↑↑↓↑↑↓... -phase and Z 2 broken phase is the first. order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.

Quantum phase transition in the transverse field Ising model on a $Delta; chain

We study quantum phase transition in the fully frustrated Δ chain Ising model under transverse fields Γ at spins on tops of the triangles and λΓ at ones on bottoms of the triangles, by using perturbation expansions, the numerical diagonalization method and a mean-field approximation with the Jordan–Wigner transformation. The system with λ=0 has a ground state with staggered order in the bottom chain for Γ>0. The transverse field at least as large as λcΓ destroys the staggered order. We calculate the critical point λc(Γ/J), where J denotes the antiferromagnetic exchange interaction, and obtain λc(Γ/J)⩽λc(+0)=0.946.

Magnetization plateau and cusp in S=1 spin ladder

Recently, the organic compound biphenyl (BIP–TENO) was synthesized and found to be the first S=1 spin ladder. The present high-field measurement up to 70 T indicates that a plateau appears in the magnetization curve at M= M s/4, where M s is the saturation magnetization. We propose possible mechanisms of the M= M s/4 plateau in BIP–TENO. The frustration in the first, second and third neighbor antiferromagnetic exchange interactions in the S=1 ladder yields the M= M s/4 plateau, with a spontaneous breaking of the translational symmetry. This can be known by use of the degenerate perturbation theory from the strong rung coupling limit. By use of the numerical diagonalization method, we revealed that the most realistic mechanism of the M= M s/4 plateau in BIP–TENO is due to the third neighbor interaction. Further theoretical analyses suggest the present mechanism should also lead to a cusp in the magnetization curve. The cusp-like anomaly in the experimental magnetization curve is a considerable evidence for our mechanism. We also discuss the M s/2 plateau problem. We show that a small rung coupling cannot yield the M s/2 plateau, which is quite different from the M=0 plateau problem of the S= 1 2 ladder.

Quantum phase transition in the transverse field Ising model on a Δ chain

Abstract We study quantum phase transition in the fully frustrated Δ chain Ising model under transverse fields Γ at spins on tops of the triangles and λΓ at ones on bottoms of the triangles, by using perturbation expansions, the numerical diagonalization method and a mean-field approximation with the Jordan–Wigner transformation. The system with λ =0 has a ground state with staggered order in the bottom chain for Γ >0. The transverse field at least as large as λ c Γ destroys the staggered order. We calculate the critical point λ c ( Γ / J ), where J denotes the antiferromagnetic exchange interaction, and obtain λ c ( Γ / J )⩽ λ c (+0)=0.946.

Exciton States in a Gaussian Confining Potential Well**The project supported by National Natural Science Foundation of China under Grant No. 10275014

We consider the problem of an electron-hole pair in a Gaussian confining potential well. This problem is treated within the effective-mass approximation framework using the method of numerical matrix diagonalization. The energy levels of the low-lying states are calculated as a function of the electron-hole effective mass ratio and the size of the confining potential.

Quantum tunneling of two coupled single-molecular magnets

Two single-molecule magnets are coupled antiferromagnetically to form a supramolecule dimer. We study the coupling effect and tunneling process by means of the numerical exact diagonalization method, and apply them to the recently synthesized supramoleculer dimer [Mn4]2 The model parameters are calculated for the dimer based on the tunneling process. The absence of tunneling at zero field and sweeping rate effect on the step height in the hysterisis loops are understood very well in this theory.

Bethe-ansatz studies of energy-level crossings in the one-dimensional Hubbard model

Motivated by Heilmann and Lieb's work, we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence of solutions for the Lieb--Wu equations with one-down spin, we solve them numerically and construct Bethe ansatz eigenstates. We thus verify all the level crossings in the spectral flows observed by the numerical diagonalization method with one down-spin. For each of the solutions we obtain its energy spectral flow along the interaction parameter U. Then, we observe that some of the energy level crossings can not be explained in terms of U-independent symmetries. Dynamical symmetries of the Hubbard model are fundamental for identifying each of the spectral lines at the level crossing points. We show that the Bethe ansatz eigenstates which degenerate at the points have distinct sets of eigenvalues of the higher conserved operators. We also show a twofold permanent degeneracy in terms of the Bethe ansatz wavefunction.

The Electron-Hole Pair in a Single Quantum Dot and Thatin a Vertically Coupled Quantum Dot**The project supported by National Natural Science Foundation of China under Grant No. 10275014

The energy spectra of low-lying states of an exciton in a single and a vertically coupled quantum dots are studied under the influence of a perpendicularly applied magnetic field. Calculations are made by using the method of numerical diagonalization of the Hamiltonian within the effective-mass approximation. We also calculated the binding energy of the ground and the excited states of an exciton in a single quantum dot and that in a vertically coupled quantum dot as a function of the dot radius for different values of the distance and the magnetic field strength.

Ferromagnetism and Superconductivity in the Multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $\Delta$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $\Delta$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_{\rho}>1$ is observed for the singlet ground state in this region.

Unambiguous relationship between the Hubbard, t–J and d–p models in one-dimension based on the Luttinger liquid theory

We examine the one-dimensional (1D) d–p model in comparison with typical 1D models such as the 1D Hubbard model and the 1D t–J model using the numerical diagonalization method combined with the Luttinger liquid theory. We calculate the spin velocity vσ, the charge velocity vρ and the Luttinger liquid parameter Kρ for each model. Using these parameters, a relationship between the models is obtained unambiguously. We find that the d–p model can be described by the Hubbard model in the wide parameter region, while it can be described by the t–J model only in the strong coupling limit.

Impurity Spin Effect on the Spin-1 Antiferromagnetic Heisenberg Chain

Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization. It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Neel-type configuration of the magnetic moment around the impurity bond. On the basis of the present results, we propose a new energy versus magnetic-field diagram.

Ground State Phase Diagram of the DistortedS=1 Kagomé Heisenberg Antiferromagnets with Single-site Anisotropy

The ground state phase transitions in the distorted S=1 kagome Heisenberg antiferromagnet (KHAF) with single-site anisotropy D are studied by the numerical exact diagonalization method. For strong easy plane anisotropy, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and large-D state is realized. The quantum phase transition between these two states is analogous to the Haldane-large-D transition in the S=1 antiferromagnetic Heisenberg chain. The combined effect of the sqrt(3) times sqrt(3) lattice distortion and single site anisotropy is also investigated. The ground state phase diagram expected from the numerical results is presented. The presence of this transition is consistent with the HSS picture of the ground state of the uniform S=1 KHAF and supports its validity.

Ground State Phase Transition in S=1 Distorted Kagomé Heisenberg Antiferromagnets

The ground state phase transition in the distorted S=1 kagom\'e Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.

Gadolinium clusters at finite temperature: exact results in the framework of a quantum Heisenberg model

The magnetic properties of clusters with N ≤ 13 atoms were investigated as a function of the temperature in the framework of Heisenberg model. The canonical partition function was calculated using all the spectrum obtained by an exact numerical diagonalization method. Interesting results are observed for the average total spin ( S ) as a function of the ratio between nearest neighbors ferromagnetic and next-nearest neighbors antiferromagnetic coupling. Our model is applied to rare-earth magnets and qualitatively describes the magnetic behavior of gadolinium clusters.