Charge degrees in the quarter-filled checkerboard lattice

For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling. An effective Hamiltonian for the limit $|t|\ll V$ is given to lowest non-vanishing order by the ring exchange ($\sim t^{3}/V^{2}$). We show that the system can equivalently be described by hard-core bosons and map the model to a confining U(1) lattice gauge theory.Comment: Proceedings of ICM200

Density-Matrix approach to a Strongly Coupled Two-Component Bose-Einstein Condensate

The time evolution equations for average values of population and relative phase of a strongly coupled two component BEC is derived analytically. The two components are two hyper-fine states coupled by an external laser that drives fast Rabi oscillations between these states. Specifically, this derivation incorporates the two-mode model proposed in [1] for the strongly coupled hyper-fine states of Rb. The fast Rabi cycle is averaged out and rate equations are derived that represents the slow dynamics of the system. These include the collapse and revival of Rabi oscillations and their subsequent dependence on detuning and trap displacement as reported in experiments of [1]. A proposal to create stable vortices is also given.Comment: 11 Latex pages, 2 figures (Figure 3 was removed and the text chnaged accordingly

Dirac, Anderson, and Goldstone on the Kagome

We show that there exists a long-range RVB state for the kagome lattice spin-1/2 Heisenberg antiferromagnet for which the spinons have a massless Dirac spectrum. By considering various perturbations of the RVB state which give mass to the fermions by breaking a symmetry, we are able to describe a wide-ranging class of known states on the kagome lattice, including spin-Peierls solid and chiral spin liquid states. Using an RG treatment of fluctuations about the RVB state, we propose yet a different symmetry breaking pattern and show how collective excitations about this state account for the gapless singlet modes seen experimentally and numerically. We make further comparison with numerics for Chern numbers, dimer-dimer correlation functions, the triplet gap, and other quantities. To accomplish these calculations, we propose a variant of the SU(N) theory which enables us to include many of the effects of Gutzwiller projection at the mean-field level.Comment: 18 pages, 6 figures; added references, minor correction

Quantized circular motion of a trapped Bose-Einstein condensate: coherent rotation and vortices

We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusodial variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained. [Changes: new numerical and analytical results are added and the representation is improved.]Comment: 13 Pages, 5 Figures, RevTe

Recurrence in 2D Inviscid Channel Flow

I will prove a recurrence theorem which says that any $H^s$ ($s>2$) solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small $H^0$ neighborhood. Periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of the author [Li, 09] on 2D Euler equation under periodic boundary conditions along both directions

Vortices in a Bose-Einstein condensate confined by an optical lattice

We investigate the dynamics of vortices in repulsive Bose-Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the OL potential relative to the magnetic trap, and depends less on the OL strength. For the cosinusoidal OL potential, a local minimum is generated at the trap's center, creating a stable equilibrium for the vortex, while in the case of the sinusoidal potential, the vortex is expelled from the center, demonstrating spiral motion. Cases where the vortex is created far from the trap's center are also studied, revealing slow outward-spiraling drift. Numerical results are explained in an analytical form by means of a variational approximation. Finally, motivated by a discrete model (which is tantamount to the case of the strong OL lattice), we present a novel type of vortex consisting of two pairs of anti-phase solitons.Comment: 10 pages, 6 figure

Doorway states and the Bose-Hubbard model

We introduce an efficient method to solve the Mott-Hubbard model. The Schr\"{o}dinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body correlations introduced by the hamiltonian, but the dimensionality of the Hilbert space is greatly reduced. We apply the doorway method to obtain the chemical potential, the on-site fluctuations and the visibility of the interference pattern arising from atoms in a one-dimensional periodic lattice. Excellent agreement with exact numerical calculations as well as recent experimental observations is found.Comment: 4 figure

Inhomogeneous d-wave superconducting state of a doped Mott insulator

Recent scanning tunneling microscope (STM) measurements discovered remarkable electronic inhomogeneity, i.e. nano-scale spatial variations of the local density of states (LDOS) and the superconducting energy gap, in the high-Tc superconductor BSCCO. Based on the experimental findings we conjectured that the inhomogeneity arises from variations in local oxygen doping level and may be generic of doped Mott insulators which behave rather unconventionally in screening the dopant ionic potentials at atomic scales comparable to the short coherence length. Here, we provide theoretical support for this picture. We study a doped Mott insulator within a generalized t-J model, where doping is accompanied by ionic Coulomb potentials centered in the BiO plane. We calculate the LDOS spectrum, the integrated LDOS, and the local superconducting gap, make detailed comparisons to experiments, and find remarkable agreement with the experimental data. We emphasize the unconventional screening in a doped Mott insulator and show that nonlinear screening dominates at nano-meter scales which is the origin of the electronic inhomogeneity. It leads to strong inhomogeneous redistribution of the local hole density and promotes the notion of a local doping concentration. We find that the inhomogeneity structure manifests itself at all energy scales in the STM tunneling differential conductance, and elucidate the similarity and the differences between the data obtained in the constant tunneling current mode and the same data normalized to reflect constant tip-to-sample distance. We also discuss the underdoped case where nonlinear screening of the ionic potential turns the spatial electronic structure into a percolative mixture of patches with smaller pairing gaps embedded in a background with larger gaps to single particle excitations.Comment: 19 pages, final versio