SU(4) Coherent Effects to the Canted Antiferromagnetic Phase in Bilayer Quantum Hall Systems at ν\nu=2

In bilayer quantum Hall (BLQH) systems at $\nu$=2, three different kinds of ground states are expected to be realized, i.e. a spin polarized phase (spin phase), a pseudospin polarized phase (ppin phase) and a canted antiferromagnetic phase (C-phase). An SU(4) scheme gives a powerful tool to investigate BLQH systems which have not only the spin SU(2) but also the layer (pseudospin) SU(2) degrees of freedom. In this paper, we discuss an origin of the C-phase in the SU(4) context and investigate SU(4) coherent effects to it. We show peculiar operators in the SU(4) group which do not exist in SU$_{\text{spin}}$(2)$\otimes$SU$_{\text{ppin}}$(2) group play a key role to its realization. It is also pointed out that not only spins but also pseudospins are ``canted'' in the C-phase.Comment: 8 pages, 4 figures and 1 tabl

Interlayer Coherence in the ν=1\nu=1 and ν=2\nu=2 Bilayer Quantum Hall States

We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $\nu=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $\nu =1$ and discovered at $\nu =2$. In particular, three different $\nu =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.Comment: 4 pages including 5 figure

Spin-Pseudospin Coherence and CP3^{3} Skyrmions in Bilayer Quantum Hall Ferromagnets

We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$\nu =2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.Comment: 4 pages including 2 figures (published version

Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"

The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant, taking into account the geometrical feature of SO(3,1) connections. A parametrization which unifies the two sectors of the physical phase space is also given.Comment: Latex 8 pages (Crucial and essential changes have been made.

PseudoSkyrmion Effects on Tunneling Conductivity in Coherent Bilayer Quantum Hall States at ν=1\nu =1

We present a mechamism why interlayer tunneling conductivity in coherent bilayer quantum Hall states at $\nu=1$ is anomalously large, but finite in the recent experiment. According to the mechanism, pseudoSkyrmions causes the finite conductivity, although there exists an expectation that dissipationless tunneling current arises in the state. PseudoSkyrmions have an intrinsic polarization field perpendicular to the layers, which causes the dissipation. Using the mechanism we show that the large peak in the conductivity remains for weak parallel magnetic field, but decay rapidly after its strength is beyond a critical one, $\sim 0.1$ Tesla.Comment: 6 pages, no figure

On the Canonical Formalism for a Higher-Curvature Gravity

Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal L}=\sqrt{-\det g_{\mu\nu}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.Comment: 11 pages, no figures, Latex fil

Magnetotransport Study of the Canted Antiferromagnetic Phase in Bilayer ν=2\nu=2 Quantum Hall State

Magnetotransport properties are investigated in the bilayer quantum Hall state at the total filling factor $\nu=2$. We measured the activation energy elaborately as a function of the total electron density and the density difference between the two layers. Our experimental data demonstrate clearly the emergence of the canted antiferromagnetic (CAF) phase between the ferromagnetic phase and the spin-singlet phase. The stability of the CAF phase is discussed by the comparison between experimental results and theoretical calculations using a Hartree-Fock approximation and an exact diagonalization study. The data reveal also an intrinsic structure of the CAF phase divided into two regions according to the dominancy between the intralayer and interlayer correlations.Comment: 6 pages, 7 figure

Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems

Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of $N$-component electrons at the integer filling factor $\nu=k\leq N$. The basic algebra is the SU(N)-extended W$_{\infty}$. A specific feature is that noncommutative geometry leads to a spontaneous development of SU(N) quantum coherence by generating the exchange Coulomb interaction. The effective Hamiltonian is the Grassmannian $G_{N,k}$ sigma model, and the dynamical field is the Grassmannian $G_{N,k}$ field, describing $k(N-k)$ complex Goldstone modes and one kind of topological solitons (Grassmannian solitons).Comment: 15 pages (no figures

Interlayer Exchange Interactions, SU(4) Soft Waves and Skyrmions in Bilayer Quantum Hall Ferromagnets

The Coulomb exchange interaction is the driving force for quantum coherence in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for the exchange interaction in bilayer quantum Hall ferromagnets, which is characterized by the SU(4) isospin structure. By taking a continuous limit, the Hamiltonian gives rise to the SU(4) nonlinear sigma model in the von-Neumann-lattice formulation. The ground-state energy is evaluated at filling factors $\nu =1,2,3,4$. It is shown at $\nu =1$ that there are 3 independent soft waves, where only one soft wave is responsible for the coherent tunneling of electrons between the two layers. It is also shown at $\nu =1$ that there are 3 independent skyrmion states apart from the translational degree of freedom. They are CP$^{3}$ skyrmions enjoying the spin-charge entanglement confined within the \LLL.Comment: 12 pages, 2 figure