Variational study of the ground state energy of theE−b 1,b 2 Jahn-Teller system

In this paper a variational method for the ground state energy approximation of theE−b ₁,b ₂ Jahn-Teller system is presented. This method is based on the choice of a suitable variational ground state wave function. This trial wave function — a correlated squeezed state — is used to account for the correlation and anharmonicity of the interaction between the two vibrational modes; the anharmonicity of both modes is taken into account by the squeeze effects of these modes. The ground state of mode 1 in this trial wave function is considered as a linear combination of the two displaced harmonic oscillators. The ground state energies for the linearE - e Jahn-Teller system calculated by this method are not only in good agreement with the exact diagonalization results, but they are also better than those from the previous analytical studies. Another conclusion which results from the presented model is the following one: the squeezing effect of mode 1 for the linearE - e Jahn-Teller system is substantially smaller, in contrast with the results which are presented in the previous analytical studies.     

Exactly solvable 1D frustrated quantum spin models

A class of the frustrated quantum s = ½ models with nearest and next nearest neighbor couplings is investigated. An exact wave function of the singlet ground state at the transition point from the ferromagnetic to the singlet state is presented. The recurrence technics of expectation value calculations is developed and the simple expressions for spin-correlation function at N → ∞ are obtained. A long range double-spiral ordering is demonstrated. We show that in one particular case the model reduces to the effective spin-1 model and the exact singlet ground state wave function is presented for this model. The behavior of the system in the vicinity of the transition point is investigated.     

Effect of frustration on spin-wave excitation spectra and ground-state properties of the quasi-one-dimensional antiferromagnetic chain with asymmetrical sublattices

We investigate the effect of frustration on spin-wave excitation spectra and the properties of the quasi-one-dimensional Heisenberg chain using a spin-wave-wave analysis, the exact diagonalization method and the density matrix renormalization group method. The results show that frustration can cause the softening of the acoustic excitation spectrum ω₃, as well as the hardening of the optical excitation spectrum ω₁. As a function of the frustration parameter α, the phase diagram exhibits a ferromagnetic phase, a narrow canted phase and a singlet phase. The results obtained from numerical methods show that the spin gap obviously opens and the tetramer-dimer state dominates the properties of the ground state in the singlet phase.     

An eigenvalue problem with limitations in a finite movable basis

An asymptotic method for taking into account the constraints of the orthogonality type when solving eigenvalue problems is developed. The features of the variational determination of eigenvalues are considered, with various finite-dimensional Hilbert subspaces being used to calculate different eigenvalues. A hydrogen molecular ion is used as an example to study the influence of the finite-dimensional approximation and basis optimization on the accuracy of determining the states of identical symmetry. Calculations have shown that the method proposed makes it possible to construct a flexible, consistent scheme for determining the energies of the ground and excited states. The total energy values obtained in a basis of 29 primitive Gaussian functions differ from exact values by 0.228 μH for the ground 1σ_g state and 0.413 μH (microhartree) for the excited 2σ_g state.     

Variational calculations of the static polarizability of H2 and of the dipole-dipole contribution to the dispersion energy between two hydrogen molecules

The convergence of variation-perturbation calculations using non-linear variation parameters has been examined for the static polarizability of H₂ and for the coefficient (C₆) of the R ^-6 term in the multipole expansion of the H₂-H₂ dispersion energy. Using a correlated ground state wavefunction, and one excited state for each of the parallel and perpendicular components of the polarizability, a single variational parameter for each state gave 96 per cent of the exact value of α_⊥ and 91 per cent of the exact value of α_‖. A second variational parameter for the parallel component gave 94 per cent of α_‖. The same procedure gave the spherical average and anisotropy of C₆ to an accuracy of about 90 per cent. By extending the calculations into the region where overlap of the orbitals of the two molecules becomes significant, it is shown for the end-on configuration that the C₆ R ^-6 term underestimates the dispersion energy near the van der Waals' minimum by roughly 10 per cent.     

NDMAP: the best material to study the Haldane's prediction

As predicted by Haldane, spin, S=1 one-dimensional (1D) Heisenberg antiferromagnet (HAF) has an energy gap between the singlet ground state and first excited triplet. On application of magnetic field, the triplet state Zeeman splits and the energy of one of the triplet state becomes zero at a critical field, H_c. Above H_c the system recovers magnetism. Then, we expect that a quasi-1D HAF will show a magnetic long-range ordering (LRO) at low temperatures due to the inter-chain coupling. This field-induced LRO has not been observed before due to complication of the crystal structure in the materials studied so far and/or technical difficulty.From a heat capacity measurement on a single crystal of an S=1 quasi-Q1D HAF, Ni(C₅H₁₄N₂)₂N₃(PF₆), we found an anomaly at a temperature in finite fields indicating a field-induced phase transition. A magnetic LRO is confirmed by a neutron diffraction measurement on the same sample. The temperature versus magnetic field phase diagram of this compound is constructed and discussed.     

Singlet–triplet oscillations and far-infrared spectrum of four-minima quantum-dot molecule

We study ground states and far-infrared spectra (FIR) of two electrons in four-minima quantum-dot molecule in magnetic field by exact diagonalization. Ground states consist of altering singlet and triplet states, whose frequency, as a function of magnetic field, increases with increasing dot–dot separation. When the Zeeman energy is included, only the two first singlet states remain as ground states. In the FIR spectra, we observe discontinuities due to crossing ground states. Non-circular symmetry induces anticrossings, and also an additional mode above ω₊ in the spin-triplet spectrum. In particular, we conclude that electron–electron interactions cause only minor changes to the FIR spectra and deviations from the Kohn modes result from the low-symmetry confinement potential.     

Local and interfacial magnetic properties of inhomogeneous finite linear chains

The Hubbard Model has been used to study the local and interfacial magnetic properties of finite inhomogeneous cluster systems. These are generally of the type, NMMMMMN, where N and M, respectively, refer to non-magnetic and magnetic atoms, of a 7-site finite chain. The applicability of the Hartree–Fock (HF) approximation is gauged via direct comparison of the ground state magnetization results derived from exact diagonalization methods. The underlying HF and exact mechanisms are compared as a function of the model parameters, with particular attention being paid to the local and interfacial (N/M interface) magnetic properties. Regimes, which exhibit favourable comparison between HF and exact results are found. Detailed inspection of the HF prediction is made and general trends established as a function of system size and model parameters.     

Modeling of synthesis and dissociation of the N<Subscript>4</Subscript> nitrogen cluster of D<Subscript>2H</Subscript> symmetry

Within the framework of multi-configurational self-consistent field (MCSCF) approximation, the ground and excited states of the N₄(D_2H) cluster of N₂ molecules are modeled from different initial states. The potential barriers to the cluster formation and dissociation are calculated. Investigations of the N₄(D_2H) electronic spectrum demonstrate that the most promising method of forming nitrogen nanostructures is compression of the excited triplet N₂ molecules.     

Bound magnetopolaron in delta GaAs quantum dot under Rashba effect

This paper presents the influence of Rashba effect on bound magnetopolaron in delta quantum dot. The unitary transformation method and the variational method of Pekar type have been used to derive the ground and first excited state energy. Due to Rashba effect, the ground and first excited states each split into two energies (spin up and down). Results show that the split up(down) energy of ground and first excited states are increasing (decreasing) function of wave vector; the spin splitting of the ground and first excited states are decreasing function of the delta parameter and the increasing function of Rashba parameter. It has also be seen that the splitting of energies levels occur around the value $q=0$. The density of probability has its minimum value at the center of the dot while it is maximal at the boundary of the dot. The decoherence has been studied through the Shannon entropy and the results show increase of entropy with time, delta parameter K, and cyclotron frequency ω_c. It also suggests a way to encrypt information and to control decoherence.     

Investigation of the magnetic properties of chains with alternating ferro-and antiferromagnetic exchange interactions in the Heisenberg model with spin S=1/2

The quantum Monte Carlo method is used to calculate the susceptibility and pairwise spin-spin correlation functions of chains with alternating ferro (K)-and antiferromagnetic (J)-exchange interactions within the Heisenberg model with spin S=1/2. From the susceptibility, the energy gap between the ground state and excited triplet states is determined or arbitrary ratios K/J. The value of the gap coincides with the Haldane gap for spin S=1 when K/J>1.25. Fiz. Tverd. Tela (St. Petersburg) 41, 1650–1651 (September 1999)     

A negatively charged exciton in a quantum disc

The properties of the bound states of the negatively charged exciton X⁻ in a quantum disc with a confined parabolic potential are studied using exact diagonalization techniques. The binding energy spectra of the ground state and the first excited state are calculated as a function of the confinement strength and the effective electron-to-hole mass ratio. The results we have obtained show that the binding energies are closely correlated to the strength of the confinement potential and the effective electron-to-hole mass ratio.     

Li2分子自旋一致激发态a3Σ+u和b3Πu的分析势能函数的从头算

使用对称性匹配簇-组态相互作用方法首次计算了Li₂分子自旋一致激发态a³Σ⁺_u和b³Π_u的离解能、平衡几何及其谐振频率。使用最小二乘法、利用Murrell-Sorbie函数形式拟合出了Li₂分子三重态的第一激发态a³Σ⁺_u 和第二激发态b³Π_u的完整势能函数，并计算了这两个态的光谱常数 (B_e, α_e, ω_e 和 ω_eχ_e) 和力常数 (f₂, f₃和f₄)。得到了Murrell-Sorbie函数形式既适用于基态、又适用于激发态的结论。将计算得到的激发态（a³Σ⁺_u和b³Π_u）的离解能、平衡几何及其谐振频率与实验结果及其它理论计算结果进行了比较。从比较的结果中可以清楚地看出，本文的计算结果在计算精度方面有很大的改进。     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

双电子二维量子点基态能量的计算

分别利用微扰法、精确的对角化方法和变分法计算了双电子二维量子点的基态能量,与早期无约束的哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.     

Effects of antisymmetric interactions in molecular iron rings

The level crossing mechanism between the ground and the first excited state of Na:Fe₆ antiferromagnetically coupled iron rings is studied by torque magnetometry down to 40 mK and in magnetic fields up to 28 T. The step width at the crossing field B_c assumes a finite value at the lowest temperatures. This fact is ascribed to the presence of level anticrossing, not expected for a ring with axial, i.e. S₆ point group, symmetry. Assuming a reduced symmetry, we revised the model Hamiltonian of such a spin system by introducing a Dzyaloshinsky-Moriya (DM) term and we show, by exact diagonalization, that DM term can account for the mixing of states with different parity. In particular, analytical as well numerical analysis show that the introduction of the DM term may contribute to the broadening of the torque step as well as for the finite energy gap at B_c observed by heat capacity in a similar ring Li:Fe₆ as previously reported [#!aclbg!#]. Received 3 September 2002 Published online 31 December 2002     

乙醇-水团簇分子形成激基缔合物及荧光发射机理研究

紫外光照射具有特殊结构的长链式乙醇-水团簇分子时,处于激发态和基态的分子形成了分子间激基缔合物,并发射荧光.根据实验结果分析和能量转移理论可知,激发态单分子和激基缔合物间形成了电子迁移洛合物并发生了能量转移.根据Mulliken理论对电子迁移洛合物进行量子力学处理,得出了团簇分子在基态和激发态能量E^b_N和E^b_E以及由于电子迁移而引起的静电相互作用能E^s;根 关键词： 荧光光谱 激基缔合物 电子迁移 乙醇-水团簇