Quantum Hall fractions in ultracold atomic vapors

Atomic vapors can be prepared and manipulated at very low densities and temperatures. When they are rotating, they can reach a quantum Hall regime in which there should be manifestations of the fractional quantum Hall effect. We discuss the appearance of the principal sequence of fractions nu =p/(p+- 1) for bosonic atoms. The termination point of this series is the paired Moore-Read Pfaffian state. Exotic states fill the gap between the paired state and the vortex lattice expected at high filling of the lowest Landau level. In fermionic vapors, the p-wave scattering typical of ultralow energy collisions leads to the hard-core model when restricted to the lowest Landau level.Comment: 7 pages, 2 figs, brief review submitted to Modern Physics Letters

Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Neel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is good agreement between DMRG data and our analytical results.Comment: 10 pages, 5 encapsulated figures, REVTeX 3.

Parafermionic states in rotating Bose-Einstein condensates

We investigate possible parafermionic states in rapidly rotating ultracold bosonic atomic gases at lowest Landau level filling factor nu=k/2. We study how the system size and interactions act upon the overlap between the true ground state and a candidate Read-Rezayi state. We also consider the quasihole states which are expected to display non-Abelian statistics. We numerically evaluate the degeneracy of these states and show agreement with a formula given by E. Ardonne. We compute the overlaps between low-lying exact eigenstates and quasihole candidate wavefunctions. We discuss the validity of the parafermion description as a function of the filling factor.Comment: 23 pages, 10 figure

Field-Induced Disorder Point in Non-Collinear Ising Spin Chains

We perform a theoretical study of a non-collinear Ising ferrimagnetic spin chain inspired by the compound Co(hfac)2NITPhOMe. The basic building block of its structure contains one Cobalt ion and one organic radical each with a spin 1/2. The exchange interaction is strongly anisotropic and the corresponding axes of anisotropy have a period three helical structure. We introduce and solve a model Hamiltonian for this spin chain. We show that the present compound is very close to a so-called disorder point at which there is a massive ground state degeneracy. We predict the equilibrium magnetization process and discuss the impact of the degeneracy on the dynamical properties by using arguments based on the Glauber dynamics.Comment: revtex 4, 10 pages, 7 figure

Pairing in ultracold Fermi gases in the lowest Landau level

We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both s-wave and p-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor in the lowest Landau level and in terms of the ratio between s- and p-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or composed of spin-singlets. In the regime with no phase separation, we give evidence for fractional quantum Hall states. Most notably, we find two distinct singlet states at the filling nu =2/3 for different interactions. One of these states is accounted for by the composite fermion theory while the other one is a paired state for which we identify two competing descriptions with different topological structure. This paired state may be an Abelian liquid of composite spin-singlet Bose molecules with Laughlin correlations. Alternatively, it may be a known non-Abelian paired state, indicated by good overlaps with the corresponding trial wavefunction. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for nu =1/2 and the permanent state of Moore and Read for nu =1. For purely repulsive interactions, we also find evidence for a gapped Halperin state at nu=2/5.Comment: 12 pages, 9 figs (best viewed in color), published version with additional evidence for a non-Abelian spin singlet state at filling nu=2/

Phases of random antiferromagnetic spin-1 chains

We formulate a real-space renormalization scheme that allows the study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement numerically the decimation procedure. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong disorder case where the physics is that of the random singlet phase.Comment: 29 pages, 12 encapsulated Postscript figures, REVTeX 3.

Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

We study the magnetic excitation spectrum of the S=1 quantum Heisenberg spin chain with Hamiltonian : H = sum_i cos(theta) S_i S_i+1 + sin(theta) (S_i S_i+1)^2. We focus on the range -pi/4 < theta < +pi/4 where the spin chain is in the gapped Haldane phase. The excitation spectrum and static structure factor is studied using direct Lanczos diagonalization of small systems and density-matrix renormalization group techniques combined with the single-mode approximation. The magnon dispersion has a minimum at q=pi until a critical value theta_c = 0.38 is reached at which the curvature (velocity) vanishes. Beyond this point, which is distinct from the VBS point and the Lifshitz point, the minimum lies at an incommensurate value that goes smoothly to 2pi/3 when theta approaches pi/4, the Lai-Sutherland point. The mode remains isolated from the other states: there is no evidence of spinon deconfinement before the point theta =+pi/4. These findings explain recent observation of the magnetization curve M approx (H -H_c)^1/4 for theta =theta_c.Comment: 14 pages, 8 encapsulated figures, REVTeX 3.