Showing papers on "Ground state published in 1989"

Two Theorems on the Hubbard Model

Abstract: In the attractive Hubbard model (and some extended versions of it) the ground state is proved to have spin angular momentum S = 0 for every (even) electron filling. In the repulsive case, and with a bipartite lattice and a half filled band, the ground state has S = 1/2∥B∣ − ∣A∥, where ∣B∣ (resp. ∣A∣) is the number of sites in the B (resp. A) sublattice. In both cases the ground state is unique. These theorems hold for all values of U, the attraction or repulsion parameter. The second theorem confirms an old, unproved conjecture in the ∣B∣ = ∣A∣ case; the generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism. Since topology is irrelevant for the proofs, the theorems hold in all dimensions without even the necessity of a periodic lattice structure.

Laser Cooling to the Zero-Point Energy of Motion

Abstract: A single trapped $^{198}\mathrm{Hg}^{+}$ ion was cooled by scattering laser radiation that was tuned to the resolved lower motional sideband of the narrow $^{2}S_{\frac{1}{2}}\ensuremath{-}^{2}D_{\frac{5}{2}}$ transition. The different absorption strengths on the upper and lower sidebands after cooling indicated that the ion was in the ground state of its confining well approximately 95% of the time.

Numerical study of the two-dimensional Hubbard model

Abstract: We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.

Valence Bond and Spin-Peierls Ground States of Low-Dimensional Quantum Antiferromagnets

Abstract: The nature of the ground state in the non-Neel phase of Heisenberg Hamiltonians on bipartite lattices will be discussed using a large -N method. Topological effects produce different spin-Peierls or valence bond solid states depending periodically on the magnitude of the spin, with periodicity given by the co-ordination number of the lattice. If time allows, topological effects and statistics of excitations for other Heisenberg and Hubbard models will also be discussed.

Motion of a single hole in a quantum antiferromagnet

Abstract: We formulate a quasiparticle theory for a single hole in a quantum antiferromagnet in the limit that the Heisenberg exchange energy is much less than the hopping matrix element, J\ensuremath{\ll}t. We consider the ground state of the spins to be either a quantum N\'eel state or a d-wave resonating-valence-bond (RVB) state. We show in a self-consistent perturbation theory that the hole spectrum is strongly renormalized by the interactions with spin excitations. The hole can be described by a narrow quasiparticle band located at an energy of order -t with a quasiparticle residue of order J/t and a bandwidth of order J. Above the quasiparticle band is an incoherent band of width of order t. Our results indicate that the energy scale for any coherent phenomenon involving the holes is \ensuremath{\delta}J, where \ensuremath{\delta} is the doping concentration. In the N\'eel state we perform a spin-wave expansion on an anisotropic Heisenberg model. In the Ising limit we reproduce previously known results and then expand perturbatively about that limit. In this expansion we find that the holes have a quasiparticle residue of ${J}_{z}$/t and a bandwidth of ${J}_{\ensuremath{\perp}}$. In the Heisenberg limit we employ a ``dominant pole'' approximation in which we ignore contributions to the self-energy from the incoherent part of the hole spectrum. A similar technique is used to study the d-wave RVB state. The relevance of our results to recent optical experiments is discussed.

Large- n limit of the Hubbard-Heisenberg model

Abstract: To gain insight into the behavior of the Hubbard model, we define a $\mathrm{SU}(n)$ invariant generalization of the Hubbard-Heisenberg model and, in the large-$n$ limit, solve it in one dimension and in two dimensions on a square lattice. In one dimension the ground state is completely dimerized near half filling. We show that this behavior agrees with a renormalization-group solution of the one-dimensional $\mathrm{SU}(n)$ Hubbard model. In two spatial dimensions we find several different ground states depending on the size of the hopping term $t$, the doping $\ensuremath{\delta}$, and the biquadratic spin interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. In particular, the undimerized "flux" or "$s+id$" phase is the ground state at half filling for sufficiently large $t$ or $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. We study the electronic and spin excitations of the various phases and comment on the relevance of the large-$n$ problem to the high-${T}_{c}$ superconductors.

Order parameter and Ginzburg-Landau theory for the fractional quantum Hall effect.

Abstract: A new order parameter with a novel broken symmetry is proposed for the fractional quantum Hall effect, with the Laughlin state as the mean-field ground state. The classical Ginzburg-Landau theory of Girvin is derived microscopically from this starting point and exhibits all the phenomenology of the fractional quantum Hall effect.

Femtosecond real-time probing of reactions. IV. The reactions of alkali halides

Abstract: The photodissociation dynamics of some alkali halides are explored via the method of femtosecond transition-state spectroscopy (FTS). The alkali halide dissociation reaction is influenced by the interaction between the covalent and the ground state ionic potential energy surfaces (PES), which cross at a certain internuclear separation. Depending upon the adiabaticity of the PES, the dissociating fragments may be trapped in a well formed by the avoided crossing of these surfaces. Here, we detail the FTS results of this class of reactions, with particular focus on the reaction of sodium iodide: NaI*-->[Na---I]°* -->Na+I. As in our first report [T. S. Rose, M. J. Rosker, and A. H. Zewail, J. Chem. Phys. 88, 6672 (1988)], we observe the dynamical motion of the wave packet along the reaction coordinate and the crossing between the covalent and ionic surfaces. The studies presented here characterize the effects of various experimental parameters, including pump and probe wavelengths, on the dynamics of the dissociation and its detection. Comparisons of the results with classical and quantum mechanical calculations are also presented.

Nonparabolicity effects in a quantum well: Sublevel shift, parallel mass, and Landau levels

Abstract: The influence of nonparabolicity on the subband structure in a quantum well is analyzed. Starting from an accurate expression for the bulk conduction-band structure expanded up to fourth order in k, we determine both the shift of the confinement energies and the energy dispersion parallel to the layers E${(\mathrm{k}}_{?}$). The resulting eigenvalue equations are of the same form as in the parabolic case, but somewhat more complicated. The anisotropy of the bulk conduction band is included, and it is found to have a larger effect in quantum wells than in the bulk. The results can be expressed in terms of the perpendicular mass, which is relevant for the determination of confinement energies, and the parallel mass, which gives the curvature of E${(\mathrm{k}}_{?}$) at the bottom of a subband. We derive approximate expressions for these masses in the form of explicit functions of the confinement energy, which is experimentally accessible. The enhancement of the parallel mass relative to the bulk mass is found to be 2--3 times stronger than that of the perpendicular mass. It is shown that the boundary conditions need to be modified in the nonparabolic case. The nonintuitive result is that the confinement energy for the ground state usually is increased relative to a similar calculation in the parabolic approximation. We include the effect of a perpendicular magnetic field and derive an analytic expression for the Landau levels. The cyclotron mass is found to increase with magnetic field and approach the parallel mass in the limit of small magnetic fields. The parallel mass is also relevant for transport parallel to the layers, density of states, and exciton properties. The agreement with experiment is encouraging. Previous theoretical approaches are critically reviewed and the differences and similarities with this work are pointed out.

A collisional-radiative model applicable to argon discharges over a wide range of conditions. I. Formulation and basic data

Abstract: A collisional-radiative model with an extended region of applicability is developed for an argon atom plasma. Atom-atom inelastic collisions and diffusion losses of the metastable states along with the electron-atom inelastic collisions and radiative processes are considered in this model, taking into account 65 effective levels. Among the analytical expressions used for the corresponding cross sections, special attention is paid to those determining the set of cross sections for excitation by electrons from the ground state, owing to the possibility of utilising the formulae recommended in kinetic modelling studies of discharges in argon or in mixtures including argon atoms. The numerical method developed makes it possible to investigate the mechanisms by which the excited levels are populated in a non-equilibrium argon plasma characterised (even in the case of a non-Maxwellian electron distribution) by a set of parameters, such as the electron kinetic temperature Te, the atom temperature Ta, the ion temperature Ti, the electron number density ne, the ground state atom population n1, the discharge tube (or the plasma column) radius R and the optical escape factors Lambda mn and Lambda m, which are dependent only on the quantities Ta, n1 and R in many cases of practical interest.

Ground-state and optical properties of Cu 2 O and CuO crystals

Abstract: The band structures of cubic ${\mathrm{Cu}}_{2}$O and monoclinic CuO crystals have been calculated by means of the first-principles orthogonalized linear combination of atomic orbitals method. Using the wave functions obtained, the frequency-dependent interband optical conductivities are also evaluated. The results show ${\mathrm{Cu}}_{2}$O to be a direct-gap semiconductor, while CuO is semiconductorlike with an intrinsic hole population at the top of the valence band (VB). By comparing with a variety of existing data, we conclude that band theory works extremely well for ${\mathrm{Cu}}_{2}$O, but is less satisfactory for CuO. This could be due to strong correlation effects for states near the top of the VB in CuO. A careful reanalysis of optical data and excitonic spectra in ${\mathrm{Cu}}_{2}$O in conjunction with our calculations suggests a complete reinterpretation of these data. A clear distinction between the intrinsic gap and the optical gap is argued. We conclude that the intrinsic gap in ${\mathrm{Cu}}_{2}$O is of the order of 0.8 eV, while the optical gap is of the order 2.0--2.3 eV. The excitonic series in ${\mathrm{Cu}}_{2}$O is due to the Coulombic attraction of the hole at the top of the VB and the electron in the next-higher conduction band (CB), not the lowest CB, because of the forbidden symmetry associated with angular-momentum conservation. This reinterpretation of the excitonic data is also consistent with a calculated low value for the static dielectric constant ${\ensuremath{\epsilon}}_{0}$ of order of 4 for ${\mathrm{Cu}}_{2}$O.

Astonomical and laboratory detection of the SiC radical

Abstract: Laboratory and space observations of a number of mm-wave rotation lines in the previously unobserved 3Pi electronic ground state of the SiC radical are discussed. Laboratory-derived frequencies, accurate to better than 0.1 ppm, are used to obtain a highly precise determination of the fine structure, rotational, centrifugal distortion, and Lambda-doubling constants of the SiC ground state. It is found that SiC is appreciably extended toward IRC+10216, with a diameter of at least 54 arcsec. 11 refs.

Studies of copper valence states with Cu L 3 x-ray-absorption spectroscopy

Abstract: We have used x-ray-absorption spectroscopy to study a series of compounds in which Cu assumes a formal valence between 0 and 3. We find that the shape, the threshold energy, and the intensity of the Cu ${L}_{3}$ absorption edge is strongly influenced by the chemical state of the Cu atoms. We use the Cu 2p x-ray-absorption spectra of a large number of Cu compounds, including sulfides, oxides, La-Sr-Cu-O compounds, a phthalocyanine complex, and various minerals to show that the presence of a strong 2p-3d excitonic transition is a fingerprint of the Cu(${d}^{9}$) contribution to the ground state. A simple ionic picture is generally inadequate to describe these compounds.

Random phase approximation in the fractional statistics gas

Abstract: The random-phase approximation for a gas of particles obeying (1/2) fractional statistics, in the context of Feynman perturbation theory performed in the fermion representation, is shown to yield a gauge-invariant Meissner effect with full screening in the ground state, a coherence length comparable with the interparticle spacing, and a linearly dispersing undamped collective mode.

Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in 2 dimensions.

Abstract: A Lanczos technique is used to study the frustrated spin-1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling J2 greater than or equal to 0. For large J2, the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of J2, the squares of order parameters associated with spin-Peierls and 'twisted'states have a peak, while a similar quantity for a chiral state shows no interesting structure.

Phase diagram of the two-dimensional negative-U Hubbard model.

Abstract: Theoretical arguments and numerical calculations are used to discuss the phase diagram of the two-dimensional negative-U Hubbard model. Our results are consistent with (1) a vanishing transition temperature at half-filling but with a ground state having both superconducting and charge-density-wave long-range order, and (2) a Kosterlitz-Thouless transition at a finite temperature into a superconducting state with power-law decay of the pairing correlations away from half-filling.

Valence bond approach to exact nonlinear optical properties of conjugated systems

Abstract: Diagrammatic valence‐bond (DVB) theory is extended to dynamic nonlinear susceptibilities of interacting π electrons in Pariser–Parr–Pople (PPP) or other quantum cell models whose correlated ground state ‖G〉 is known. Corrections φ(1)(ω) and φ(2)(ω2,ω1) to ‖G〉 due to oscillating electric fields are found directly as linear combinations of VB diagrams. Any nonlinear optical coefficient is reduced to matrix elements that implicitly include all excited states, as verified for shorter polyenes. Static and dynamic χ(3) coefficients for cis and trans polyenes to N=12 carbons illustrate the importance of retaining the full spectrum. The coefficients βijk(ω,ω) for second harmonic generation are found for polar molecules like aniline and nitroaniline. Divergent responses are treated by lifetimes Γ for the resonant states, as shown for third harmonic generation in hexatriene with Γ=0 and in octatetraene with Γ>0. Electron–electron interactions reverse the sign of γijkl(ω,ω,ω) in linear polyenes, except for the large...

On Green's function calculations of the static self-energy part, the ground state energy and expectation values

Abstract: The necessity to determine the static self‐energy part Σ(∞) in many‐body Green’s function studies of atomic and molecular ionization introduces difficulties affecting both the accuracy and the efficiency of the method. We show how this bottleneck can be overcome under an approximation obtained by truncating the Dyson expansion for the one‐particle Green’s function G(ω). Here the essential computational step consists of an inversion or a Lanczos diagonalization of constant Hermitian secular matrices associated with the dynamical self‐energy part M(ω). Both methods are very practical and efficient as is demonstrated in an exemplary application to the CO molecule. The same approximation and numerical techniques apply also to the problem of extracting ground state information from G(ω), i.e., correlation energy and expectation values of single‐particle operators.

Statistics of the excitations of the resonating-valence-bond state

Abstract: By extending recent proposals for choosing the phases in resonating-valence-bond ground states to the case of excited states, we show for these wave functions that the hole excitations are charged, spinless fermions and the spin excitations are neutral, spin-(1/2 bosons. We also show that for a system with periodic boundary conditions, all states are at least fourfold degenerate.

For even-even nuclides throughout the periodic table

Abstract: Adopted values for the excitation energy, &(3;), of the first 3- state of even-even nuclides are tabulated. Values of the reduced electric-octupole transition probability, B(E3;O: + 3;), from the ground state to this state, as determined from Coulomb excitation, lifetime measurements, inelastic electron scattering, deformation parameters /3s obtained from angular distributions of inelastically scattered nucleons and light ions, and other miscellaneous procedures are listed in separate tables. Adopted values for B(E3;O: + 3;) are presented in the final table, together with the E3 transition strengths, in Weisskopf units, and the product EA3;) X B(E3;O: --* 3;), expressed as a percentage of the energyweighted E3 sum-rule strength. An evaluation is made of the reliability of B(E3;O: + 31) values deduced from deformation parameters &. The literature has been covered to March 1988.

New limits on the electron electric dipole moment from cesium.

Abstract: The electric-dipole moment (edm) of the ground state of cesium has been measured using a two-laser method that does not require the presence of an external B field. The measured value ${\mathit{d}}_{\mathrm{Cs}}$=(-1.8\ifmmode\pm\else\textpm\fi{}6.7\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ e cm implies that the electron EDM is ${\mathit{d}}_{\mathit{e}}$=(-1.5\ifmmode\pm\else\textpm\fi{}5.5\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}26}$ e cm. This result represents more than an order-of-magnitude improvement over all previous limits.

Numerical Studies on the Hubbard Model and the t - J Model in One- and Two-Dimensions

Abstract: Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t - J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t - J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t - J and th...

Ground-state properties of third-row elements with nonlocal density functionals

Abstract: The cohesive energy, the lattice parameter, and the bulk modulus of third-row elements are calculated using the Langreth-Mehl-Hu (LMH), the Perdew-Wang (PW), and the gradient expansion functionals. The PW functional is found to give somewhat better results than the LMH functional and both are found to typically remove half the errors in the local-spin-density (LSD) approximation, while the gradient expansion gives worse results than the local-density approximation. For Fe both the LMH and PW functionals correctly predict a ferromagnetic bcc ground state, while the LSD approximation and the gradient expansion predict a nonmagnetic fcc ground state.

Ground State(s) of the Spin-Boson Hamiltonian

Abstract: We establish that the finite temperature KMS states of the spin-boson hamiltonian have a limit as the temperature drops to zero. Using recent advances on the one-dimensional Ising model with long range, 1/r2, interactions, we prove qualitative properties of the ground state(s) in the ohmic case. We show (i) the asymptotics of the critical coupling as the bare energy gap goes to zero and to infinity, (ii) a jump in the order parameter, and (iii) that the number of bosons is finite below and infinite at and above the critical coupling strength.

Collisional losses from a light-force atom trap

Abstract: We have studied the collisional loss rates for very cold cesium atoms held in a spontaneous-force optical trap. In contrast with previous work, we find that collisions involving excitation by the trapping light fields are the dominant loss mechanism. We also find that hyperfine-changing collisions between atoms in the ground state can be significant under some circumstances. PACS numbers: 32.80.Pj, 34.50.Rk Spontaneous-force light traps' have provided a way to obtain relatively deep static traps for neutral atoms. These allow one to produce samples containing large numbers of very cold atoms. In this paper we present an experimental study of the collisions which eject atoms from such a trap. These collisions are of considerable interest because the temperatures of the trapped atoms (10 K) are far lower than in usual atomic collision experiments. The theory of such low-energy collisions and their novel features have been discussed by several authors. Perhaps the most notable feature is that the collision times are very long, and the collision dynamics are dominated by long-range interactions and spontaneous emission. These collisions also have important implications with regard to potential uses of optically trapped atoms. For many applications the maximum density that can be obtained is a critical parameter, and these collisions limit the attainable density. There have been two experimental studies of collisions in optical traps. Gould et al. measured the cross section for associative ionization of sodium. However, there is no evidence that this process is significant in limiting trapped-atom densities, and for some atoms, including cesium, it is energetically forbidden. Prentiss et al. studied the collisional losses which limited the density of sodium atoms which were held in a spontaneous-force trap. Their surprising and unexplained results were a direct stimulus for our work. In particular, they observed no dependence of the loss rate on the intensity of the trapping light. This was quite surprising, because a ground and an excited atom interact at long range via the strong 1/r resonant dipole interaction, and a portion of the excited-state energy can be converted into sufficient kinetic energy to allow the atoms to escape from the trap. By comparison, two atoms in their ground states interact only through a much weaker short-range 1/r Van der Waals attraction, and even when such collisions occur, they may not produce significant kinetic energy to cause trap loss. This implies that the dominant collisional loss mechanism would involve the excited atomic states, and thus depend on the intensity of the light which causes such excitations. In this paper we present measurements which show that, in contrast with Ref. 9, the collisional loss rate has a marked dependence on the trap laser intensity. We will present strong circumstantial evidence that the dependence at very low intensities is due to hyperfinechanging collisions between ground-state atoms. We believe that the loss rates at higher intensities are associated with collisions involving excited states, and are the type discussed by Gallagher and Pritchard. As discussed in Ref. 7, these collisions are very different from normal ground-excited-state atomic collisions in which two initially distant atoms, A and A approach, collide, and separate in a time much less than the radiative lifetime of the excited state. In contrast, for these very-low-temperature collisions the absorption and emission of radiation in the midst of the collision drastically alter the motion. In particular, if the excitation takes place when the two atoms are far apart (R) 1000 A) they will reradiate before being pulled into the small-R region where energy transfer occurs. However, if they are sufficiently close when excited, they can be pulled close enough together for substantial potential energy to be transferred into kinetic energy before decaying. The two dominant transfer processes are excited-state fine-structure changes and radiative redistribution. In the first, A changes its fine-structure state in the collision and the pair acquire a fine-structureinterval worth of kinetic energy. The second process, radiative redistribution, refers to A Areemitting a -photon which, because of the A-A* attractive potential, has substantially less energy than that of the photon which was initially absorbed. This energy difference is transferred to the subsequent kinetic energy of the ground-state atoms. The trap loss rate depends on the probability of exciting such "close" A-A pairs, and this probability is determined by the frequency and intensity of the exciting radiation. Light which is tuned to the red of the atomic resonance frequency, vo, excites pairs which are closer together (and shifted in energy) and thus is more eN'ective at causing trap loss than light which is at vo. We tested this hypothesis by examining how the loss