Abstract:
We apply the theory of elasticity to study the effects of skyrmion mass on lattice dynamics in quantum Hall systems. We find that massive Skyrme lattices behave like a Wigner crystal in the presence of a uniform perpendicular magnetic field. We make a comparison with the microscopic Hartree-Fock results to characterize the mass of quantum Hall skyrmions at $\nu=1$ and investigate how the low temperature phase of Skyrme lattices may be affected by the skyrmion mass.

Abstract:
The topological solitons, or ``skyrmions'', in a planar ferromagnet experience a Magnus force proportional to the product of their velocity and the surrounding magnetization. It has been suggested that the charged quasiparticles near filling factor $\nu=1$ in the $GaAs$ quantum Hall effect are skyrmions. If so we might expect this spin-induced Magnus force to act on the quasiparticles in addition to the Lorentz force they experience because of their charge. We show that this is not the case, and that the Magnus and Lorentz forces are merely different descriptions of the same physical effect.

Abstract:
We present a microscopic theory of skyrmions in the monolayer quantum Hall ferromagnet. It is a peculiar feature of the system that the number density and the spin density are entangled intrinsically as dictated by the W$%_{\infty}$ algebra. The skyrmion and antiskyrmion states are constructed as W$_{\infty }$-rotated states of the hole-excited and electron-excited states, respectively. They are spin textures accompanied with density modulation that decreases the Coulomb energy. We calculate their excitation energy as a function of the Zeeman gap and compared the result with experimental data.

Abstract:
We report on a microscopic theory of the Skyrmion states which occur in the quantum Hall regime. The theory is based on the identification of Skyrmion states in this system with zero-energy eigenstates of a hard-core model Hamiltonian. We find that for $N_{\phi}$ orbital states in a Landau level, a set of Skyrmions states with orbital degeneracy $N_{\phi}-K$ and spin quantum number $S = N/2 -K$ exists for each nonnegative integer $K$. The energetic ordering of states with different $K$ depends on the interaction potential.

Abstract:
An improved composite-boson theory of quantum Hall ferromagnets is proposed. It is tightly related with the microscopic wave-function theory. The characteristic feature is that the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. It presents a powerful tool to analyze excited states within the \LLLd. Excitations include a Goldstone mode and nonlocal topological solitons. Solitons are vortices and Skyrmions carrying the U(1) and SU(2) topological charges, respectively. Their classical configurations are derived from their microscopic wave functions. The activation energy of one Skyrmion is estimated, which explains experimental data remarkably well.

Abstract:
We report on a study of the classical field theory description of charged skyrmions in quantum Hall ferromagnets. The appropriate field theory is a non-linear $\sigma$ model generalized to include Coulomb and Zeeman interaction terms. We have tested the range of validity of the classical field theory by comparing with microscopic descriptions of the single skyrmion state based on the Hartree-Fock approximation, exact diagonalization calculations, and many-body trial wavefunctions. We find that the field theory description is accurate for skyrmions with moderate spin quantum numbers ($\gtrsim 10$) although, as expected, it fails qualitatively for small spin quantum numbers.

Abstract:
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.

Abstract:
We propose an improved composite-boson theory of quantum Hall ferromagnets, where the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. In this scheme skyrmions appear merely as generic excitations confined in the lowest Landau level. We evaluate the excitation energy of one skyrmion. Our theoretical estimation accounts for the activation-energy data due to Schmeller et al. remarkably well.

Abstract:
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.

Abstract:
We report on a study of the charged-skyrmion or spin-texture excitations which occur in quantum Hall ferromagnets near odd Landau level filling factors. Particle-hole symmetry is used to relate the spin-quantum numbers of charged particle and hole excitations and neutral particle-hole pair excitations. Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau level quantum numbers, and the thicknesses of the two-dimensional electron layers. For the case of $\nu$ near three we suggest the possibility of first order phase transitions with increasing Zeeman coupling strength from a many skyrmion state to one with many maximally spin-polarized quasiparticles.