Anomaly-Free Supersymmetric SO(2N+2)/U(N+1) sigma-Model Based on the SO(2N+1) Lie Algebra of the Fermion Operators

The extended supersymmetric (SUSY) sigma-model has been proposed on the bases of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have investigated the SUSY sigma-model on the Kaehler manifold, the coset space SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the potential in the SO(2N)/U(N) coset space to that in the SO(2N+2)/U(N+1) coset space. It is equivalent to the generalized density matrix whose diagonal-block part is related to a reduced scalar potential with a Fayet-Ilipoulos term. The f-deformed reduced scalar potential is optimized with respect to vacuum expectation value of the sigma-model fields and a solution for one of the SO(2N+1) group parameters has been obtained. The solution, however, is only a small part of all solutions obtained from anomaly-free SUSY coset models. To construct the coset models consistently, we must embed a coset coordinate in an anomaly-free spinor representation (rep) of SO(2N+2) group and give corresponding Kaehler and Killing potentials for an anomaly-free SO(2N+2)/U(N+1) model based on each positive chiral spinor rep. Using such mathematical manipulation we construct successfully the anomaly-free SO(2N+2)/U(N+1) SUSY sigma-model and investigate new aspects which have never been seen in the SUSY sigma-model on the Kaehler coset space SO(2N)/U(N). We reach a f-deformed reduced scalar potential. It is minimized with respect to the vacuum expectation value of anomaly-free SUSY sigma-model fields. Thus we find an interesting f-deformed solution very different from the previous solution for an anomaly-free SO(2.5+2)/(SU(5+1)*U(1)) SUSY sigma-model.Comment: 24 pages, no fiure

Nonlinear Bogolyubov-Valatin transformations and quaternions

In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.

Competition between spin and charge polarized states in nanographene ribbons with zigzag edges

Effects of the nearest neighbor Coulomb interaction on nanographene ribbons with zigzag edges are investigated using the extended Hubbard model within the unrestricted Hartree-Fock approximation. The nearest Coulomb interaction stabilizes a novel electronic state with the opposite electric charges separated and localized along both edges, resulting in a finite electric dipole moment pointing from one edge to the other. This charge-polarized state competes with the peculiar spin-polarized state caused by the on-site Coulomb interaction and is stabilized by an external electric field.Comment: 4 pages; 4 figures; accepted for publication in Phys. Rev. B; related Web site: http://staff.aist.go.jp/k.harigaya/index_E.htm

Broken-symmetry-adapted Green function theory of condensed matter systems:towards a vector spin-density-functional theory

The group theory framework developed by Fukutome for a systematic analysis of the various broken symmetry types of Hartree-Fock solutions exhibiting spin structures is here extended to the general many body context using spinor-Green function formalism for describing magnetic systems. Consequences of this theory are discussed for examining the magnetism of itinerant electrons in nanometric systems of current interest as well as bulk systems where a vector spin-density form is required, by specializing our work to spin-density-functional formalism. We also formulate the linear response theory for such a system and compare and contrast them with the recent results obtained for localized electron systems. The various phenomenological treatments of itinerant magnetic systems are here unified in this group-theoretical description.Comment: 17 page

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Origin of line broadening in the electronic absorption spectra of conjugated polymers: Three-pulse-echo studies of MEH-PPV in toluene

Integrated three-pulse stimulated echo peak shift data are compared for N,N-bis-dimethylphenyl-1-2,4,6,8-perylenetetracarbonyl diamide and poly[2-(2'-ethylhexyloxy)-5-methoxy-1,4-phenylenevinylene] (MEH-PPV) in toluene solvent. These two molecules represent a model probe of solvation dynamics and a prototypical soluble, electroluminescent conjugated polymer, respectively. The results indicate that it is inappropriate to describe the linear absorption spectrum of MEH-PPV as being primarily inhomogeneously broadened. Conformational disorder along the polymer backbone gives rise to an ensemble of polyene electronic oscillators that are strongly coupled to each other. As a consequence, fluctuations in the electronic energy gap on a time-scale of 50-fs derive primarily from bath-mediated exciton scattering. The data reported here provide an explanation for the broad, structureless electronic absorption of MEH-PPV. This interpretation provides a valuable insight into the nature of the initial photoexcited state, and the efficient population of the emissive state