Stripe State in the Lowest Landau Level

The stripe state in the lowest Landau level is studied by the density matrix renormalization group (DMRG) method. The ground state energy and pair correlation functions are systematically calculated for various pseudopotentials in the lowest Landau level. We show that the stripe state in the lowest Landau level is realized only in a system whose width perpendicular to the two-dimensional electron layer is smaller than the order of magnetic length.Comment: 4 pages, 6 figures, to appear in J. Phys. Soc. Jpn. vol.73 No.1 (2004

Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites

The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the electrons {\em within} each cell is taken into account exactly (including exchange and correlation effects), and the interaction {\em between} the cells is in second order (dipole) van der Waals approximation. No further approximations are made, in particular Landau level mixing and {\em in}complete spin polarization are accounted for. Therefore, our calculation comprises a, roughly speaking, complementary description of the bubble phase (in the special case of one and two electrons per bubble), which was proposed by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation. The phase diagram shows that in GaAs the paired phase is energetically more favorable than the single electron phase for, roughly speaking, filling factor $f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohr radii (for a more precise statement see Fig.s 4 and 5). If we start within the paired phase and increase magnetic field or decrease density, the pairs first undergo some singlet- triplet transitions before they break.Comment: 11 pages, 7 figure

Spin-Wave Theory of the Spiral Phase of the t-J Model

A graded H.P,realization of the SU(2|1) algebra is proposed.A spin-wave theory with a condition that the sublattice magnetization is zero is discussed.The long-range spiral phase is investigated.The spin-spin correlator is calculated.Comment: 17 page

Evolution of nu=1nu=1 Bilayer Quantum Hall Ferromagnet

The natures of the ground state in a $\nu_{\rm T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connection to the modified composite fermion theory is discussed

Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.Comment: 5 pages, to appear in J. Phys. Soc. Jpn. Vol.73, No.8 (2004

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $\nu\equiv N/N_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $\nu$, there is a zero temperature {\it phase transition} between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states

Effect of a tilted magnetic field on the orientation of Wigner crystals

We study the effect of a tilted magnetic field on the orientation of Wigner crystals by taking account of the width of a quantum well in the $z$-direction. It is found that the cohesive energy of the electronic crystal is always lower for the $[110]$ direction parallel to the in-plane field. In a realistic sample, a domain structure forms in the electronic solid and each domain orients randomly when the magnetic field is normal to the quantum well. As the field is tilted an angle, the electronic crystal favors to align along a preferred direction which is determined by the in-plane magnetic field. The orientation stabilization is strengthened for wider quantum wells as well as for larger tilted angles. Possible consequence of the tilted field on the transport property in the electronic solid is discussed

Effects of Next-Nearest-Neighbor Repulsion on One-Dimensional Quarter-Filled Electron Systems

We examine effects of the next-nearest-neighbor repulsion on electronic states of a one-dimensional interacting electron system which consists of quarter-filled band and interactions of on-site and nearest-neighbor repulsion. We derive the effective Hamiltonian for the electrons around wave number \pm \kf (\kf: Fermi wave number) and apply the renormalization group method to the bosonized Hamiltonian. It is shown that the next-nearest-neighbor repulsion makes 4\kf-charge ordering unstable and suppresses the spin fluctuation. Further the excitation gaps and spin susceptibility are also evaluated.Comment: 19 pages, 8 figures, submitted to J. Phys. Soc. Jp

Stability of the Excitonic Phase in Bilayer Quantum Hall Systems at Total Filling One -- Effects of Finite Well Width and Pseudopotentials --

The ground state of a bilayer quantum Hall system at $\nu_{\rm T}=1$ with model pseudopotential is investigated by the DMRG method. Firstly, pseudopotential parameters appropriate for the system with finite layer thickness are derived, and it is found that the finite thickness makes the excitonic phase more stable. Secondly, a model, where only a few pseudopotentials with small relative angular momentum have finite values, is studied, and it is clarified how the excitonic phase is destroyed as intra-layer pseudopotential becomes larger. The importance of the intra-layer repulsive interaction at distance twice of the magnetic length for the destruction of the excitonic phase is found.Comment: 7 pages, 7 figure

Field theory of spin-singlet quantum Hall states

We formulate a field theory for a class of spin-singlet quantum Hall states (the Haldane-Rezayi state and its variants) which have been proposed for the quantized Hall plateaus observed at the second lowest Landau level. A new essential ingredient is a class of super Chern-Simons field. We show that the known properties of the states are consistently described by it. We also give a 2+1 dimensional hierarchical construction. Implications of the proposal are discussed and a new physical picture of composite particles at the second lowest Landau level emerges.Comment: RevTex, 5 pages, 1 figur