Competing orders in the generalized Hund chain model at half-filling

By using a combination of several non-perturbative techniques -- a one-dimensional field theoretical approach together with numerical simulations using density matrix renormalization group -- we present an extensive study of the phase diagram of the generalized Hund model at half-filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases like Ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg Hubbard ladder with interchain hopping. Our results obtained from a weak coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.Comment: 26 pages, 14 figure

Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms

A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of $N$ for attractive interactions at half-filling. The analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin $N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.Comment: 4 pages, 4 figure

Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at half filling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p-band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2I+1) symmetry which depend only on the nuclear spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when I=1/2,5/2,9/2,..., which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I(=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2I+1)-symmetry

Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture

We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin ${\cal S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd. We point out that the $N=1,2$ cases do \emph{not} have the generic properties of each family. The metallic phase for $N$ odd and larger than 1 has a quasi-long range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even $N$ further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann {\it et al.} [Pollmann {\it et al.}, arXiv:0909.4059 (2009)].Comment: 25 pages, 20 figure

Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain

The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg chain are investigated by means of a low-energy approach and large-scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg chain is dimerized with a twofold degenerate ground state. On top of this gapful phase, we find the emergence of a nondegenerate gapped phase with hidden (Z(2) x Z(2))(2) symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)(1) universality class

miR-CATCH: microRNA capture affinity technology.

Several experimental methods exist to explore the microRNA (miRNA) regulome. These methods almost exclusively focus on multiple targets bound to a single, or perhaps a few miRNAs of interest. Here, we describe a microRNA capture affinity technology (miR-CATCH) which uses an affinity capture oligonucleotide to co-purify a single target messenger RNA (mRNA) together with all its endogenously bound miRNAs. This bench-top method is similar to RNA immunoprecipitation (RIP) and provides an experimental alternative to computational miRNA target prediction

Quantum Computing and Quantum Simulation with Group-II Atoms

Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and quantum simulation. In these systems, it is possible to encode qubits in nuclear spin states, which are decoupled from the electronic state in the $^1$S$_0$ ground state and the long-lived $^3$P$_0$ metastable state on the clock transition. This leads to quantum computing scenarios where qubits are stored in long lived nuclear spin states, while electronic states can be accessed independently, for cooling of the atoms, as well as manipulation and readout of the qubits. The high nuclear spin in some fermionic isotopes also offers opportunities for the encoding of multiple qubits on a single atom, as well as providing an opportunity for studying many-body physics in systems with a high spin symmetry. Here we review recent experimental and theoretical progress in these areas, and summarise the advantages and challenges for quantum computing and quantum simulation with group-II atoms.Comment: 11 pages, 7 figures, review for special issue of "Quantum Information Processing" on "Quantum Information with Neutral Particles

Die kirchliche Gemeindevertretung nach ihrem Amt und Geist : eine Predigt, gehalten zu Soest am 18ten October 1835 vor der versammelten hochwürdigen Synode der Provinz Westphalen

von J. H. J. Nonn