Model Wave Functions Research Articles

Lattice construction of pseudopotential Hamiltonians for fractional Chern insulators

Fractional Chern insulators are new realizations of fractional quantum Hall states in lattice systems without orbital magnetic field. These states can be mapped onto conventional fractional quantum Hall states through the Wannier state representation (Phys. Rev. Lett. 107, 126803 (2011)). In this paper, we use the Wannier state representation to construct the pseudopotential Hamiltonians for fractional Chern insulators, which are interaction Hamiltonians with certain ideal model wavefunctions as exact ground states. We show that these pseudopotential Hamiltonians can be approximated by short-ranged interactions in fractional Chern insulators, and that their range will be minimized by an optimal gauge choice for the Wannier states. As illustrative examples, we explicitly write down the form of the lowest pseudopotential for several fractional Chern insulator models including the lattice Dirac model and the checkerboard model with Chern number 1, and the d-wave model and the triangular lattice model with Chern number 2. The proposed pseudopotential Hamiltonians have the 1/3 Laughlin state as their groundstate when the Chern number C=1, and a topological nematic (330) state as their groundstate when C=2. Also included are the results of an interpolation between the d-wave model and two decoupled layers of lattice Dirac models, which explicitly demonstrate the relation between C=2 fractional Chern insulators and bilayer fractional quantum Hall states. The proposed states can be verified by future numerical works, and in particular provide a model Hamiltonian for the topological nematic states that have not been realized numerically.

Covariant spectator theory of np scattering: Deuteron magnetic moment

The deuteron magnetic moment is calculated using two model wave functions obtained from 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents which are automatically generated by the nuclear force model used in these fits. After normalizing the wave functions, nearly identical predictions are obtained: model WJC-1, with larger relativistic P-state components, gives 0.863(2), while model WJC-2 with very small P-state components gives 0.864(2) These are about 1\% larger than the measured value of the moment, 0.857 n.m., giving a new prediction for the size of the $\rho\pi\gamma$ exchange, and other purely transverse interaction currents that are largely unconstrained by the nuclear dynamics. The physical significance of these results is discussed, and general formulae for the deuteron form factors, expressed in terms of deuteron wave functions and a new class of interaction current wave functions, are given.

Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene

We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A frozen regime can occur for strong disorder in these systems, wherein a single wavefunction presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a Quantum Hall critical metal. For the case of two valleys and non-abelian disorder, we verify predictions of conformal field theory. Our results for the non-abelian case imply that both delocalization and conformal invariance are topologically-protected for multivalley topological superconductor surface states.

Accuracy of simple folding model in the calculation of the direct part of real α−α interaction potential

The direct part of real α−α interaction potential is calculated in the simple folding model using density-dependent Brink–Boeker effective interaction. The simple folding potentials calculated from the short- and finite-range components of this effective interaction are compared with their corresponding double folding results obtained from the oscillator model wave function to establish the relative accuracy of the model. It is found that the direct part of real α−α interaction potential calculated in the simple folding model is reliable.

Superconductivity of composite particles in a two-channel Kondo lattice.

Emergence of odd-frequency s-wave superconductivity is demonstrated in the two-channel Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum MonteCarlo method. Around half filling of the conduction bands, divergence of an odd-frequency pairing susceptibility is found, which signals instability toward the superconductivity. The corresponding order parameter is equivalent to a staggered composite-pair amplitude with even frequencies, which involves both localized spins and conduction electrons. A model wave function is constructed for the composite order with the use of symmetry operations such as charge conjugation and channel rotations. Given a certain asymmetry of the conduction bands, another s-wave superconductivity is found that has a uniform order parameter. The Kondo effect in the presence of two channels is essential for both types of unconventional superconductivity.

Electron electric dipole moment and hyperfine interaction constants for ThO

A recently implemented relativistic four-component configuration interaction approach to study P- and T-odd interaction constants in atoms and molecules is employed to determine the electron electric dipole moment effective electric field in the Ω=1 first excited state of the ThO molecule. We obtain a value of Eeff=75.2GVcm with an estimated error bar of 3% and 10% smaller than a previously reported result (Skripnikov et al., 2013). Using the same wavefunction model we obtain an excitation energy of TvΩ=1=5410 (cm-1), in accord with the experimental value within 2%. In addition, we report the implementation of the magnetic hyperfine interaction constant A|| as an expectation value, resulting in A||=-1339 (MHz) for the Ω=1 state in ThO. The smaller effective electric field increases the previously determined upper bound (Baron et al., 2014) on the electron electric dipole moment to |de|<9.7×10-29ecm and thus mildly mitigates constraints to possible extensions of the Standard Model of particle physics.

Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the (k + 1)-Equals Ideal

We show that for Jack parameter \alpha = -(k+1)/(r-1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k+1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in case r = 2 identifies the span of the relevant Jack polynomials with the S_n-invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the (k+1)-equals arrangement in the case when the number of coordinates n is at most 2k+1. In general, our conjecture predicts the graded S_n-equivariant Betti numbers of the ideal of the (k+1)-equals arrangement with no restriction on the number of ambient dimensions.

Hall viscosity of hierarchical quantum Hall states

Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter τ, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor ν=2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.5 MoreReceived 8 January 2014Revised 26 February 2014DOI:https://doi.org/10.1103/PhysRevB.89.125303©2014 American Physical Society

Observation ofB¯(s)0→J/ψf1(1285)Decays and Measurement of thef1(1285)Mixing Angle

Decays of Bs and B0 mesons into J/\psi \pi +\pi -\pi +\pi - final states, produced in pp collisions at the LHC, are investigated using data corresponding to an integrated luminosity of 3/fb collected with the LHCb detector. B^0_(s) -> J\psi f_1(1285) decays are seen for the first time, and the branching fractions are measured. Using these rates, the f_1(1285) mixing angle between strange and non-strange components of its wave function in the q-qbar structure model is determined to be \pm (24.0^{+3.1+0.6}_{-2.6-0.8}) degrees. Implications on the possible tetraquark nature of the f_1(1285) are discussed.

Predicting a prior for Planck

The quantum state of the universe combined with the structure of the landscape potential implies a prior that specifies predictions for observations. We compute the prior for CMB related observables given by the no-boundary wave function (NBWF) in a landscape model that includes a range of inflationary patches representative of relatively simple single-field models. In this landscape the NBWF predicts our classical cosmological background emerges from a region of eternal inflation associated with a plateau-like potential. The spectra of primordial fluctuations on observable scales are characteristic of concave potentials, in excellent agreement with the Planck data. By contrast, alternative theories of initial conditions that strongly favor inflation at high values of the potential are disfavored by observations in this landscape.

Condensate Phase Microscopy

We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.

Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in Laughlin Quantum Hall Fluids

We construct model wave functions for a family of single-quasielectron states supported by the ν = 1/3 fractional quantum Hall fluid. The charge e* = e/3 quasielectron state is identified as a composite of a charge-2e* quasiparticle and a -e* quasihole, orbiting around their common center of charge with relative angular momentum nℏ > 0, and corresponds precisely to the "composite fermion" construction based on a filled n = 0 Landau level plus an extra particle in level n > 0. An effective three-body model (one 2e* quasiparticle and two -e* quasiholes) is introduced to capture the essential physics of the neutral bulk excitations.

Magnetoresistive polyaniline/multi-walled carbon nanotube nanocomposites with negative permittivity

Contrary to the observed positive giant magnetoresistance (GMR) in as-received multi-walled carbon nanotubes (MWNTs), pure polyaniline (PANI) synthesized with Cr(vi) as oxidant and MWNTs/PANI nanocomposites with ammonium persulfate (APS) as oxidant, a room temperature negative GMR of around -2% was reported in MWNTs/PANI nanocomposites with Cr(vi) as oxidant. Different from a frequency switch of permittivity from negative to positive in MWNTs/PANI nanocomposites with APS as oxidant, unique negative permittivity was observed in MWNTs/PANI nanocomposites with Cr(vi) as oxidant within the measured frequency range from 20 to 2 × 10(6) Hz. The obtained unique negative permittivity was explained by the plasma frequency from the Drude model, at which the permittivity changes from negative to positive and the material changes from a metamaterial to an ordinary dielectric medium. The observed positive and negative GMR behaviors in these disordered systems as verified by the temperature dependent resistivity exploration were well explained through a wave-function shrinkage model and orbital magnetoconductivity theory by calculating the changed localization length (a0).

Magnetoresistive conductive polymer-tungsten trioxide nanocomposites with ultrahigh sensitivity at low magnetic field

The effect of conductive polymer matrix including polyaniline (PANI) and polypyrrole (PPy) on the magnetoresistance (MR) behaviors in the variable range hopping (VRH) regime has been investigated in the disordered polymer nanocomposites containing tungsten trioxide (WO3) nanoparticles. These nanocomposites have demonstrated ultrahigh MR sensitivity at low magnetic field regime. The observed positive MR has been well explained by the wave-function shrinkage model. The conductive polymer matrix has shown different effects on the MR behaviors of the nanocomposites. The WO3/PANI nanocomposites have a lower localization length (a0) and density of states at the Fermi level (N(EF)), and higher average hopping distance (Rhop) and average hopping energy (W) compared with those of the WO3/PPy nanocomposites.

Single-mode approximation for quantum Hall states with broken rotational symmetry

A topological phase can often be represented by a corresponding wavefunction (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wavefunction fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We demonstrate the recovery of the variational parameter in a single-mode approximation, which is consistent with the recently proposed geometric consideration of the quantum Hall phases.

Many-body study of a quantum point contact in the fractional quantum Hall regime atν=5/2

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor 5/2 we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wavefunction we find equality of neutral and charged velocities for the Pfaffian state both bosonic and fermionic.

Spectroscopic factors and asymptotic normalization coefficients for0p-shell nuclei: Recent updates

Extended tables are presented for spectroscopic factors, asymptotic normalization coefficients and rms radii of one-nucleon overlap functions for $0p$-shell nuclei calculated in the source term approach using shell model wave functions. The tabulated data includes both new results and updates on previously published values. They are compared with recent results obtained in ab initio calculations, and with experimental data, where available. The reduction of spectroscopic factors with respect to traditional shell model values as well as its neutron-proton asymmetry is also discussed.

OPTOMECHANICS OF LEVITATED DIELECTRIC PARTICLES

We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this review, we will introduce the current status of optical trapping of dielectric particles in air and vacuum, Brownian motion of an optically trapped particle at room temperature, Feedback cooling and cavity cooling of the Brownian motion. We will also discuss about using optically trapped dielectric particles for studying macroscopic quantum mechanics and ultrasensitive force detection. Applications range from creating macroscopic Schrödinger's cat state, testing objective collapse models of quantum wavefunctions, measuring Casimir force, searching short-range non-Newtonian gravity, to detect gravitational waves.

Interplay between the02+resonance and the nonresonant continuum of the drip-line two-neutron halo nucleus22C

The breakup cross section (BUX) of 22C by 12C at 250 MeV/nucleon is evaluated by the continuum-discretized coupled-channels method incorporating the cluster-orbital shell model (COSM) wave functions. Contributions of the low-lying 0+_2 and 2+_1 resonances predicted by COSM to the BUX are investigated. The 2+_1 resonance gives a narrow peak in the BUX, as in usual resonant reactions, whereas the 0+_2 resonant cross section has a peculiar shape due to the coupling to the nonresonant continuum, i.e., the Fano effect. By changing the scattering angle of 22C after the breakup, a variety of shapes of the 0+_2 resonant cross sections is obtained. Mechanism of the appearance of the sizable Fano effect in the breakup of 22C is discussed.

Hexavalent chromium synthesized polyaniline nanostructures: Magnetoresistance and electrochemical energy storage behaviors

In this work, the oxidant Cr(VI) dose was observed to have influenced the polyaniline (PANI) nanostructures as well as the crystallization structure. The temperature dependent resistivity study revealed a quasi 3-dimensional variable range hopping (VRH) electrical conduction mechanism. The permittivity was found to be affected by the PANI nanostructures. The observed positive MR at room temperature in the synthesized PANI samples was analyzed by the wave-function shrinkage model. The electrochemical energy storage was investigated using the cyclic voltammetry (CV) and galvanostatic charge–discharge measurements. The highest gravimetric capacitance of 298.5 F g−1 was obtained in the prepared PANI sample using 3 mmol K2Cr2O7 derived from the CV at a scan rate of 5 mV s−1 and the maximum value of gravimetric capacitance of 330.2 F g−1 was achieved in the galvanostatic charge–discharge measurements at a current density of 0.5 A g−1. After applying an external magnetic field, the capacitance decreased due to the observed positive magnetoresistance phenomenon. The cyclic stability studies revealed that the synthesized PANI samples exhibited good durability and retained around 80% of the capacitance even after 1000 charge–discharge galvanostatic cycles.