Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.     

Control of spin state in CdSe quantum dots by coupling with magnetic semiconductor quantum dots

We studied spin states of CdSe quantum dots (QDs) coupled with CdMnSe QDs by probing circular polarization of photoluminescence spectrum under external magnetic fields. The bandgap energies of CdSe and CdMnSe QDs are close to each other and photoluminescence mainly originates from CdSe QDs due to relatively low radiation efficiency of CdMnSe QDs. The photoluminescence lifetime as well as its intensity was decreased with increasing magnetic field, which was ascribed to the increase in the ground state wavefunctions in CdMnSe QDs. The decrease was more pronounced for spin down electrons, which was explained by the difference in spin up and down wave functions under magnetic fields. Our results show that the spin state of CdSe QDs can be manipulated by coupling with CdMnSe QDs.     

The phase diagram and hidden order for generalized spin ladders

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the [Formula: see text] chain with competing nn and nnn interactions, the [Formula: see text] chain with alternating exchange and the antiferromagnetic (AF) S = 1 chain. The Majumdar - Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the AF S = 1 chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar - Ghosh points are in the same phase as the AF S = 1 chain.     

Quasiperiodic Heisenberg antiferromagnets in two dimensions

We describe some of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have Néel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented and discussed. The effects of introducing geometrical disorder on the magnetic properties are discussed.     

Interacting Boson Approach to the Low-Dimensional Quant urn Antiferrornagnets: a Variational Monte-Carlo Study

We present a spin-1/2 antiferromagnetic Reisenberg model in an interacting boson representation exactly by using modified Holstein-Primakoff transformation. For interacting boson systems on one-dimensional linear chains and square lattices, we perform Monte-Carlo calculations using the well-established Jastrow-type trial wavefunction. We find that the ground state energies and spin correlations agree well with other numerical and theoretical results.     

Realization of a Ramsey-Bordé matter wave interferometer on the molecule

We show first results and systematic investigations of a matter wave interferometer with the K₂ molecule, using a transition between the electronic ground state X and the state b . This spin forbidden transition is observable due to spin-orbit coupling between the states b and A . The experimental results are compared with numerical simulations, which show the power of the interferometer to observe small phase shifts by weak interactions. Received 13 March 2000     

Extremal optimization for Sherrington-Kirkpatrick spin glasses

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using ±J bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of ω=2/3 for the finite-size correction exponent, and of ρ=3/4 for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent.     

Adiabatic switching approach to multidimensional supersymmetric quantum mechanics for several excited states

We present a time-dependent method for determining several approximate excited-state energies and wave functions using a vectorial approach to multidimensional supersymmetric quantum mechanics. First, a vectorial approach is used to generate the tensor sector two Hamiltonian, which is isospectral with the original scalar sector one Hamiltonian above the ground state of the sector one Hamiltonian. We construct a time-dependent Hamiltonian interpolating between the scalar sector one Hamiltonian and the tensor sector two Hamiltonian. Then, we can adiabatically switch from the ground state of the sector one Hamiltonian to the ground state of the sector two Hamiltonian by solving the time-dependent Schrödinger equation. In addition, by employing an initial wave packet orthogonal to that leading to the ground state of sector two, we also obtain the first-excited state of sector two. Construction of the orthogonal sector one states is trivial due to the tensor nature of sector two. The ground and first-excited states of the sector two Hamiltonian can be used with the charge operator to obtain the first two excited state wave functions of the sector one Hamiltonian. Excellent computational results are obtained for two-dimensional nonseparable degenerate and nondegenerate systems.     

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.     

Ionization of atoms by charged particles

Ionization of hydrogen atom by charged particle impact are studied at different collisional energies and the total and differential cross sections are calculated. In case of light particle impact the final-state wave function here considers all three two-body interactions on an equal footing and satisfies the exact Coulomb boundary conditions. The spin asymmetries are also found and the values are compared with other existing results. For heavy particle impact a final continuum state wave function which incorporates distortion due to the Coulomb fields of both the projectile and the target nuclei is employed. In this case the target hydrogen atom is considered in its ground as well as metastable 2s state. The results thus obtained are compared with the existing experimental findings as well as other theoretical predictions.     

Hartree-Fock ground state of the three-dimensional electron gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.     

计算顺磁-铁磁相变临界磁场的一种方法

利用线性自旋波方法并结合Hellmann-Feynman定理引入一种计算量子磁性系统临界磁场的方法.计算两种特殊模型的临界磁场,并将理论结果与数值结果进行比较,理论值与数值结果高度吻合,验证了理论方法的准确性.     

Ferromagnetic Ordering of Energy Levels

We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the Lieb–Mattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin subspace. Our main result is a proof of this conjecture for the spin-1/2 Heisenberg XXX and XXZ ferromagnets in one dimension. Our proof has two main ingredients. The first is an extension of a result of Koma and Nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain. For the second part of the proof we use the Temperley–Lieb algebra to calculate, in a suitable basis, the matrix elements of the Hamiltonian restricted to each subspace of the highest weight vectors with a given total spin. We then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume. Our method also shows that the first excited state of the XXX ferromagnet on any finite tree has one less than maximal total spin.     

Evaluation of entanglement measures in spin systems with the random phase approximation

We discuss a general formalism based on the mean field plus random phase approximation (RPA) for the evaluation of entanglement measures in the ground state of spin systems. The method provides a tractable scheme for determining the entanglement entropy as well as the negativity of finite subsystems, which becomes analytic in the case of systems with translational invariance, in one or D dimensions. The approach improves as the spin increases, and also as the interaction range or connectivity increases. Illustrative results for different types of entanglement entropies (single site, block and comb) in the ground state of a small spin lattice with ferromagnetic type XY couplings in a transverse field are shown and compared with the exact numerical result. Effects arising from symmetry breaking at the mean field level are also discussed.     

Fission barriers at high angular momentum and the ground state rotational band of the nucleus 254No

We study the superheavy nucleus 254No in the framework of the Hartree-Fock-Bogoliubov approximation with the finite-range density-dependent Gogny force, at zero and high angular momentum. The properties of the ground state rotational band and the fission barriers are discussed as a function of angular momentum. We found a two-humped barrier up to spin values of (30-40)Planck's over 2pi and a one-humped barrier for higher spins. We reproduce fairly well with the binding energy, the ground state deformation, the gamma-ray energies, and the bound on the fission barrier height measured at high spin.     

Half-polarized quantum hall states

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.     

Quantum-dot ground-state energies and spin polarizations: soft versus hard chaos

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations" that arise from the residual screened Coulomb interaction are very sensitive to the degree of chaos. It leads to ground state energies and spin polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.