Mean-field Ground State Research Articles

Universality and Anomalous Mean-Field Breakdown of Symmetry-Breaking Transitions in a Coupled Two-Component Bose-Einstein Condensate

We study both mean-field and full quantum dynamics of symmetry-breaking transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By controlling s-wave scattering lengths and the coupling strength, it is possible to stimulate SBTs between normal and spontaneously polarized ground states. In static transitions, the probability maxima of full quantum ground states correspond to the mean-field ground states. In dynamical transitions, due to the vanishing of excitation gaps, the mean-field dynamics shows universal scalings obeying the Kibble-Zurek mechanism. Both mean-field and full quantum defect modes appear as damped oscillations, but they appear at different critical points and undergo different oscillation regimes. The anomalous breakdown of mean-field dynamics induced by SBTs depends on the approaching direction.

Collectivity-induced quenching of signatures for shell closures

Mass differences are an often used as signature and measure for shell closure. Using the angular-momentum projected generator coordinate method and the Skyrme interaction SLy4, we analyze the modification of mass differences due to static deformation and dynamic fluctuations around the mean-field ground state.

Quantum-fluctuation-driven coherent spin dynamics in small condensates

We have studied the quantum spin dynamics of small condensates of cold sodium atoms. For a condensate initially prepared in a mean-field ground state, we show that coherent spin dynamics is purely driven by quantum fluctuations of collective spin coordinates and can be tuned by quadratic Zeeman coupling and magnetization. This dynamics in small condensates can be probed in a high-finesse optical cavity where the temporal behaviors of the excitation spectra of a coupled condensate-photon system reveal the time evolution of populations of atoms at different hyperfine spin states.

Gapless Spin Liquids on the Three-Dimensional Hyperkagome Lattice ofNa4Ir3O8

Recent experiments indicate that Na4Ir3O8, a material in which s=1/2 Ir local moments live on a three-dimensional "hyperkagome" lattice of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wave functions studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on this lattice. We point out implications of this proposal for thermodynamic properties and discuss possible weak instabilities of the spinon Fermi surfaces.

COUPLING OF SURFACE AND VOLUME DIPOLE OSCILLATIONS INC60MOLECULES

We first give a short review of the "local-current approximation" (LCA), derived from a general variation principle, which serves as a semiclassical description of strongly collective excitations in finite fermion systems starting from their quantum-mechanical mean-field ground state. We illustrate it for the example of coupled translational and compressional dipole excitations in metal clusters. We then discuss collective electronic dipole excitations in C60molecules (Buckminster fullerenes). We show that the coupling of the pure translational mode ("surface plasmon") with compressional volume modes in the semiclasscial LCA yields semi-quantitative agreement with microscopic time-dependent density functional (TDLDA) calculations, while both theories yield qualitative agreement with the recent experimental observation of a "volume plasmon".

Mean-field treatment of polymer chains trapped between surfaces and penetrable interfaces

We study the exact solutions for the problem of adsorption of polymers in a system containing two interfaces within the mean-field ground-state dominance approximation both for penetrable and nonpenetrable interfaces. We discuss the case of saturation of the polymer double layer for the limiting case of zero bulk concentration. Here, the exact solution is controlled by a single scaling variable which describes the coupling between the interfaces due to the polymer chains. For the case of penetrable interfaces we obtain a nonmonotonous behavior of the amount of adsorbed polymers as a function of the distance between the interfaces. This leads to a high- and a low-energy phase for the double layer with respect to the amount of polymers localized. At the saturation point, the force acting between the interfaces is strictly attractive and monotonously decaying toward zero for increasing interface distance for both types of interfaces. The exact solution for the chemical equilibrium state of the polymer double layer with a semidilute bulk state is governed by two scaling variables and explicit concentration dependence can be removed. The scaling variables describe the ratio between the interface distance and the bulk correlation length and the ratio between the localization length of the interfaces and the bulk correlation length, respectively. Using the exact solution on intervals of constant potentials opens the possibility to treat various localization problems for polymer chains using the appropriate boundary conditions.

Pygmy and giant dipole resonances in Ni isotopes

The isovector giant and pygmy dipole resonances in even-even Ni isotopes are studied within the framework of a fully consistent relativistic random-phase approximation built on the relativistic mean field ground state. An additional isoscalar-isovector nonlinear coupling term is adopted in the standard effective mean field Lagrangian, which could modify the density dependence of the symmetry energy and soften the symmetry energy at the saturation density without changing the agreement with experimentally existing data of ground state properties. We found that the centroid energy of the isovector giant dipole resonance is tightly correlated to the neutron skin thickness. In contrast, the centroid energy of the isovector pygmy resonance is insensitive to the density dependence of the symmetry energy by tuning the isoscalar-isovector nonlinear coupling.

α-cluster structure and exotic states in a self-consistent model for light nuclei

In this paper we examine to what extent traces of alpha-clustering can be found in mean-field ground states of $n\alpha$-nuclei from Be8 through Ar36 as well as in some superdeformed states in S32, Ar36, and Ca40. For this purpose we calculate the overlap of the mean-field Slater determinant with one containg pure Gaussians and perfect spin and isospin symmetry, optimizing the overlap by varying the alpha-particle positions and radii. In some cases a coherent sum over different configurations is also employed. We find quite large overlaps for some of the lighter systems that diminish for nuclei above Ne20 but again strong clustering in Ar36.

Spin-Wave Theory of the Multiple-Spin Exchange Model on a Triangular Lattice in a Magnetic Field: 3-Sublattice Structures

We study the spin wave in the S =1/2 multiple-spin exchange model on a triangular lattice in a magnetic field within the linear spin-wave theory. We take only two-, three-, and four-spin exchange interactions into account and restrict ourselves to the region where a coplanar three-sublattice state is the mean-field ground state. We found that the Y-shape ground state survives quantum fluctuations and the phase transition to a phase with a 6-sublattice structure occurs with softening of the spin wave. We estimated the quantum corrections to the ground state sublattice magnetizations due to zero-point spin-wave fluctuations.

Finite-temperature momentum distribution of a trapped Fermi gas

We present measurements of the temperature-dependent momentum distribution of a trapped Fermi gas consisting of $^{40}$K in the BCS-BEC crossover regime. Accompanying theoretical results based upon a simple mean-field ground state are compared to the experimental data. Non-monotonic effects associated with temperature, $T$, arise from the competition between thermal broadening and a narrowing of the distribution induced by the decrease in the excitation gap $\Delta(T)$ with increasing $T$.

Vortex lattices in rotating atomic Bose gases with non-local interactions

We study the groundstates of rotating atomic Bose gases with non-local interactions. We focus on the weak-interaction limit of a model involving s - and d -wave interactions. With increasing d -wave interaction, the mean-field groundstate undergoes a series of transitions between vortex lattices of different symmetries (triangular, square, “stripe” and “bubble” crystal phases). We discuss the stability of these phases to quantum fluctuations. Using exact diagonalization studies, we show that with increasing d -wave interaction, the incompressible Laughlin state at filling factor ν = 1 / 2 is replaced by compressible stripe and bubble states.

Low-temperature magnetization of (Ga,Mn)As semiconductors

We report on a comprehensive study of the ferromagnetic moment per Mn atom in (Ga,Mn)As ferromagnetic semiconductors. Theoretical discussion is based on microscopic calculations and on an effective model of Mn local moments antiferromagnetically coupled to valence band hole spins. The validity of the effective model over the range of doping studied is assessed by comparing with microscopic tight-binding/coherent-potential approximation calculations. Using the virtual crystal $\mathbf{k}∙\mathbf{p}$ model for hole states, we evaluate the zero-temperature mean-field contributions to the magnetization from the hole kinetic and exchange energies, and magnetization suppression due to quantum fluctuations of Mn moment orientations around their mean-field ground state values. Experimental low-temperature ferromagnetic moments per Mn are obtained by superconducting quantum interference device and x-ray magnetic circular dichroism measurements in a series of (Ga,Mn)As semiconductors with nominal Mn doping ranging from $\ensuremath{\sim}2$ to 8%. Hall measurements in as-grown and annealed samples are used to estimate the number of uncompensated substitutional Mn moments. Based on our comparison between experiment and theory we conclude that all these Mn moments in high quality (Ga,Mn)As materials have nearly parallel ground state alignment.

Ground-state description of a single vortex in an atomic Fermi gas: From BCS to Bose–Einstein condensation

We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein condensation. Our starting point is the BCS-Leggett mean field ground state for which a BdG approach is microscopically justified. At strong coupling, we demonstrate that this approach is analytically equivalent to the Gross-Pitaevskii description of vortices in true bosonic systems. We analyze the sizable density depletion found for the unitary regime and relate it to the presence of unoccupied (positive energy) quasi-bound states at the core center.

Quantum dimer models and effective Hamiltonians on the pyrochlore lattice

We study a large-$N$ deformation of the $S=1∕2$ pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading nontrivial order. In this limit, the ground state manifold---while extensively degenerate---breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the $1∕N$ expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.

Vortex lattices in Bose-Einstein condensates: From the Thomas-Fermi regime to the lowest-Landau-level regime

We consider a periodic vortex lattice in a rotating Bose-Einstein condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we solve numerically the 2D Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.

Strongly Correlated 5fElectrons: Spectral Functions and Mean-Field Ground States

Model spectral functions for 5 f systems are calculated within Cluster Perturbation Theory. The low-energy spectra exhibit dispersive quasiparticle peaks co-existing with an incoherent background. Within the present model the dual character of the 5 f electrons arises from strong intra-atomic correlations. The ground states of extended 5 f systems are analyzed treating the intra-atomic correlations within mean-field theory. The calculations confirm the qualitative results derived by exactly diagonalizing the Hamiltonian for small clusters. A characteristic feature of the spectral functions in systems with strong intra-atomic correlations are high-energy peaks associated with transitions into excited atomic multiplets. First theoretical results for UPd 2 Al 3 are presented. The calculations start from LDA conduction bands accounting for the intra-atomic correlations among the 5 f electrons in terms of an atomic-like selfenergy.

Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice

We propose that by exciting ultra cold atoms from the zeroth to the first Bloch band in an optical lattice, novel multi-flavor bosonic Hubbard Hamiltonians can be realized in a new way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band structure calculations, we determine the parameters entering these Hamiltonians and derive the mean field ground state phase diagram for two effective Hamiltonians (2D, two-flavors and 3D, three flavors). Further, we estimate the stability of atoms in the first band using second order perturbation theory and find lifetimes that can be considerable (10-100 times) longer than the relevant time scale associated with inter-site hopping dynamics, suggesting that quasi-equilibrium can be achieved in these meta-stable states.

Some Aspects of Nuclear Structure in Relativistic Approach**The project supported by National Natural Science Foundation of China under Grant Nos. 10235020 and 10275094 and The State Key Research Development Program under Grant No. G200077407

The nucleon effective interaction in the nuclear medium is investigated in the framework of the Dirac–Brueckner–Hartree–Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.

Coexistence of spin-density wave and d-wave superconducting order parameter

We study the properties of a spin-density-wave antiferromagnetic mean-field ground state with d-wave superconducting correlations. This ground state always gains energy by Cooper pairing. It would fail to superconduct at half-filling due to the antiferromagnetic gap although its particle-like excitations would be Bogolyubov-BCS quasiparticles consisting of coherent mixtures of electrons and holes. More interesting and relevant to the superconducting cuprates is the case when antiferromagnetic order is turned on weakly on top of the superconductivity. This would correspond to the onset of antiferromagnetism at a critical doping. In such a case a small gap proportional to the weak antiferromagnetic gap opens up for nodal quasiparticles, and the quasiparticle peak would be discernible. We evaluate numerically the absorption by nodal quasiparticles and the local density of states for several ground states with antiferromagnetic and d-wave superconducting correlations.

Isoscalar Giant Resonances of 120Sn in the QuasiparticleRelativistic Random Phase Approximation

The quasiparticle relativistic random phase approximation (QRRPA)is formulated based on the relativistic mean field ground state inthe response function formalism. The pairing correlations aretaken into account in the Bardeen–Cooper–Schrieffer approximation with aconstant pairing gap. The numerical calculations are performed in thecase of various isoscalar giant resonances of nucleus 120Sn withparameter set NL3. The calculated results show that the QRRPAapproach could satisfactorily reproduce the experimental data ofthe energies of low-lying states.