Explicit Wave Functions Research Articles

FRACTIONAL QUANTUM HALL STATES WITH NEGATIVE FLUX: EDGE MODES IN SOME ABELIAN AND NON-ABELIAN CASES

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general, quantum Hall states have many edge states. Here, we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction ν = 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor ν = 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally, we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve, in all cases, explicit derivative operators diminishing the angular momentum of the system.

Exact quantization of a superparticle inAdS5×S5

As a step toward deeper understanding of the AdS/CFT correspondence, exact quantization of a Brink-Schwarz superparticle in the AdS_5 x S^5 background with Ramond-Ramond (RR) flux is performed from the first principle in the phase space formulation. It includes the construction of the quantum Noether charges for the psu(2,2|4) superconformal symmetry and by solving the superconformal primary conditions we obtain the complete physical spectrum of the system with the explicit wave functions. The spectrum agrees precisely with the supergravity results, including all the Kaluza-Klein excitations. Our method and the result are expected to shed light on the eventual quantization of a superstring in this important background.

Quantum Hall quasielectron operators in conformal field theory

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.

Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. II. Application to environment-induced nonadiabatic dynamics

The non-Markovian approach developed in the companion paper [Hughes et al., J. Chem. Phys. 131, 024109 (2009)], which employs a hierarchical series of approximate spectral densities, is extended to the treatment of nonadiabatic dynamics of coupled electronic states. We focus on a spin-boson-type Hamiltonian including a subset of system vibrational modes which are treated without any approximation, while a set of bath modes is transformed to a chain of effective modes and treated in a reduced-dimensional space. Only the first member of the chain is coupled to the electronic subsystem. The chain construction can be truncated at successive orders and is terminated by a Markovian closure acting on the end of the chain. From this Mori-type construction, a hierarchy of approximate spectral densities is obtained which approach the true bath spectral density with increasing accuracy. Applications are presented for the dynamics of a vibronic subsystem comprising a high-frequency mode and interacting with a low-frequency bath. The bath is shown to have a striking effect on the nonadiabatic dynamics, which can be rationalized in the effective-mode picture. A reduced two-dimensional subspace is constructed which accounts for the essential features of the nonadiabatic process induced by the effective environmental mode. Electronic coherence is found to be preserved on the shortest time scale determined by the effective mode, while decoherence sets in on a longer time scale. Numerical simulations are carried out using either an explicit wave function representation of the system and overall bath or else an explicit representation of the system and effective-mode part in conjunction with a Caldeira-Leggett master equation.

Energy Gaps in the 4f135d1 Manifold and Multiple Spontaneous Emissions in Yb2+-Doped CsCaBr3

Multiple spontaneous 4f(13)5d(1) --> 4f(14) emissions are predicted in Yb(2+)-doped CsCaBr(3) crystals by ab initio quantum chemical calculations. Four emission bands are found at 23,900, 26,600, 34,600, and 43,900 cm(-1) that should be experimentally observable at low temperatures. The first, third, and fourth bands are slow, electric dipole forbidden emissions that can be described as spin-forbidden. The second band is a fast, electric dipole-allowed emission that cannot be described as spin-allowed, but as spin-enabled; its radiative emission lifetime is 400 ns. Large energy gaps (23 900, 4600, 4000 cm(-1), respectively), relative to the maximum local phonon energies calculated (around 185 cm(-1)), are found below the emitting levels of the slow bands, which indicates that these states should be significantly stable and multiphonon relaxation to the lower states should be negligible. A smaller gap (2600 cm(-1)) separates the states of the fast band, which should result in a temperature dependent competition between radiative and nonradiative decay. Differential correlation between 4f-4f and 4f-5d pairs, splitting of the 5d shell by interactions with the host, and spin-orbit effects within the 4f(13) subshell, are found to be responsible for the existence of the gaps, which, in turn, split the absorption spectrum into four groups of separate bands, three of which could lie below the host absorption threshold. The quantum chemical methods employed make use of explicit wave functions expanded in terms of flexible basis sets, multiconfigurational self-consistent-field and multireference second-order perturbation methods to account for nondynamic and dynamic electron correlation, scalar and relativistic terms in the (YbBr(6))(4-) defect cluster Hamiltonian, and quantum mechanical embedding potentials to represent the host crystal.

A discrete quantum model of the harmonic oscillator

We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bound, whereas the spectra of position and of momentum are a denumerable non-degenerate set of points in [− 1, 1] that depends on the deformation parameter q ∊ (0, 1). We provide its explicit wavefunctions, both in position and momentum representations, in terms of the discrete q-Hermite polynomials. We build a Hilbert space with a unique measure, where an analogue of the fractional Fourier transform is defined in order to govern the time evolution of this discrete oscillator. In the limit when q → 1−, one recovers the ordinary quantum harmonic oscillator.

One-dimensional fermionic gases with attractivep-wave interaction in a hard-wall trap

We investigate the ground state of the one-dimensional fermionic system enclosed in a hard-wall trap with attractive contact $p$-wave interactions. Based on the Bethe ansatz method, the explicit wave function is derived by numerically solving the Bethe ansatz equations for the full physical regimes $(\ensuremath{-}\ensuremath{\infty}\ensuremath{\le}{c}_{F}\ensuremath{\le}0)$. With the exact wave function some quantities which are important in many-body physics are obtained, including the one-body density matrix and the momentum distribution of the ground state for finite system. It is shown that the shell structure of the density profiles disappears with the increase of the interaction and in the fermionic Tonks-Girardeau limit the density distribution shows the same behavior as that of an ideal Bose gas. However, the one-body density matrix and the momentum distribution exhibit completely different structures compared with their bosonic counterparts.

The [formula omitted] components and the magnetic moments of the charmed and the bottomed baryons

We give the explicit wave functions of the q q q q q ¯ components of the C = + 1 , J = 1 / 2 charmed baryons, Σ c , Λ c and Ξ c a , and calculate the magnetic moments by adding the 5q components contributions, and we also compute the magnetic moments of the Σ b and Σ b ∗ baryons. The influence of the additional light and strange q q ¯ pairs is investigated. As we know, the constituent quark masses of the charm and beauty quarks are much heavier than that of the light and strange quarks, consequently, the hidden flavor contributions to the baryons magnetic moments may be significant. What is interesting is that the inclusion of the q q q q q ¯ components contributions leads to different Λ c + , Ξ c a + and Ξ c a 0 magnetic moments, all of which are predicted to be the same value 0.38 μ N on the basis of the classical qqq quark model. And it is shown that the differences of these magnetic moments are independent of the constituent mass of the charm quark.

Calculation of Vibrational Infrared Intensities and Raman Activities Using Explicit Anharmonic Wave Functions

Methods for automatic computation of IR intensities and Raman activities are described using vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) wave functions. Inclusion of effects due to anharmonicity in the potential energy and property surfaces are found to improve the results substantially as compared to experimental data. Sample calculations employing water and formaldehyde are presented, allowing for comparison between different vibrational methods. The convergence with respect to excitation level in VCI and the extent of mode coupling in the potential and property expansions is investigated. In addition, different electronic methods used for generating the potential and property surfaces, namely CCSD, CCSD(T), DFT/B3LYP, and DFT/CAM-B3LYP have been compared. Details of the potential and property surfaces may have significant effects on the IR and Raman intensities.

Explicit monodromy of Moore–Read wavefunctions on a torus

We construct the wavefunctions for the Moore–Read ν = 5/2 quantum Hall state on a torus in the presence of two quasiholes. These explicit wavefunctions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. The result agrees with the recent discussion by Oshikawa et al (Ann. Phys.at press). Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in some of the ground states.

Charge excitations inSU(n)spin chains: Exact results for the1∕r2model

We study the one- and two-holon excitations of the SU(3) Kuramoto-Yokoyama model on the level of explicit wave functions, and generalize the calculations to the case of $\mathrm{SU}(n)$. We obtain the exact energies and the single-holon momenta, which we find fractionally spaced according to fractional statistics with statistical parameter $g=1∕n$.

Wavefunctions for topological quantum registers

We present explicit wavefunctions for quasi-hole excitations over a variety of non-abelian quantum Hall states: the Read–Rezayi states with k ⩾ 3 clustering properties and a paired spin-singlet quantum Hall state. Quasi-holes over these states constitute a topological quantum register, which can be addressed by braiding quasi-holes. We obtain the braid properties by direct inspection of the quasi-hole wavefunctions. We establish that the braid properties for the paired spin-singlet state are those of ‘Fibonacci anyons’, and thus suitable for universal quantum computation. Our derivations in this paper rely on explicit computations in the parafermionic conformal field theories that underly these particular quantum Hall states.

Collective modes and skyrmion excitations in grapheneSU(4)quantum Hall ferromagnets

Graphene exhibits quantum Hall ferromagnetism in which an approximate SU(4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU(4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU(4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge $\pm 1$ for {\em any} integer filling, and that skyrmions are the lowest energy charged excitations for graphene Landau level index $|n| \le 3$. We also show that the skyrmion lattice states which occur near integer filling factors support four gapless collective mode branches in the presence of full SU(4) symmetry. Comparisons are made with the more familiar SU(2) quantum Hall ferromagnets studied previously.

Exact two-holon wave functions in the Kuramoto-Yokoyama model

We construct the explicit two-holon eigenstates of the SU(2) Kuramoto-Yokoyama model at the level of explicit wave functions. We derive the exact energies and obtain the individual holon momenta, which are quantized according to the half-Fermi statistics of the holons.

Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap

We investigate the ground state of the system of $N$ bosons enclosed in a hard-wall trap interacting via a repulsive or attractive $\ensuremath{\delta}$-function potential. Based on the Bethe ansatz method, the explicit ground state wave function is derived and the corresponding Bethe ansatz equations are solved numerically for the full physical regime from the Tonks limit to the strongly attractive limit. It is shown that the solution takes a different form in different regime. We also evaluate the one body density matrix and second-order correlation function of the ground state for finite systems. In the Tonks limit the density profiles display the Fermi-like behavior, while in the strongly attractive limit the Bosons form a bound state of $N$ atoms corresponding to the $N$-string solution. The density profiles show the continuous crossover behavior in the entire regime. Further, the correlation function indicates that the Bose atoms bunch closer as the interaction constant decreases.

Optical spectra of trivalent lanthanides in LiYF 4 crystal

Systematic calculations of multiplet energy levels of all trivalent lanthanides in LiYF 4 (YLF) crystal were performed using two completely different approaches: diagonalization of the commonly used semi-empirical Hamiltonian and a fully relativistic discrete-variational multi-electron (DV-ME) method which is based on a first-principles configuration-interaction (CI) calculation program using molecular spinors obtained by the discrete-variational Dirac–Slater (DV-DS) calculations. The energy level diagrams within 4 f n electron configurations were obtained by the former method, while those including both 4 f n and 4 f n− 15 d 1 configurations were obtained by the latter. Using the explicit many-electron wave functions, the absorption spectra of Pr 3+, Ho 3+, and Tm 3+ in YLF were calculated and compared with the experimental data.

Matrix Kadomtsev Petviashvili equation: matrix identities and explicit non-singular solutions

A new version of the Backlund–Darboux transformation for the matrix Kadomtsev–Petviashvili (KP) equation is used to construct and study explicit multi-parameter solutions and wavefunctions (in terms of the matrix exponents). A class of the self-adjoint non-singular solutions of KP I is introduced using the controllability notion from the system theory. A subclass of the rationally decaying self-adjoint non-singular solutions is studied, in particular. Several results prove new in the scalar case also.

Solution to the Rarita-Schwinger equations

A systematical method is presented for solving the relativistic wave equations for particles of arbitrary spin. Explicit helicity relativistic wave functions for particles with arbitrary spin are derived rigorously.

Solution to the Bargmann-Wigner equation for a half-integral spin

A rigorous method to solve the Bargmann-Wigner equation for an arbitrary half-integral spin is presented and explicit relativistic wavefunctions for an arbitrary half-integral spin are deduced.

Two-legt−Jladder: A spin liquid generated by Gutzwiller projection of magnetic bands

The ground state of the two-leg Heisenberg ladder is identified as a resonating-valence-band-RVB type spin liquid, which is generated by Gutzwiller projection of tight-binding bands with flux $\ensuremath{\pi}$ per plaquet. Explicit trial wave functions for the magnon and hole excitations are formulated in terms of spinons and holons. The spinon-holon bound state is shown to violate P and T. This is interpreted as a manifestation of fractional statistics.