Hidden symmetry and quantum phases in spin-3/2 cold atomic systems

Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic systems with hyperfine spin $F=3/2$, which may be realized with atoms of $^{132}$Cs, $^9$Be, $^{135}$Ba, $^{137}$Ba, and $^{201}$Hg. A {\it generic} SO(5) or isomorphically, $Sp(4)$) symmetry is proved in such systems with the s-wave scattering interactions in optical traps, or with the on-site Hubbard interactions in optical lattices. Various important features from this high symmetry are studied in the Fermi liquid theory, the mean field phase diagram, and the sign problem in quantum Monte-Carlo simulations. In the s-wave quintet Cooper pairing phase, the half-quantum vortex exhibits the global analogue of the Alice string and non-Abelian Cheshire charge properties in gauge theories. The existence of the quartetting phase, a four-fermion counterpart of the Cooper pairing phase, and its competition with other orders are studied in one dimensional spin-3/2 systems. We also show that counter-intuitively quantum fluctuations in spin-3/2 magnetic systems are even stronger than those in spin-1/2 systems

Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling

We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.Comment: slightly shortened and reorganized versio

Bond-order modulated staggered flux phase for the t−Jt{-}J model on the square lattice

Motivated by the observation of inhomogeneous patterns in some high-T$_c$ cuprate compounds, several variational Gutzwiller-projected wave-functions with built-in charge and bond order parameters are proposed for the extended $t-J-V$ model on the square lattice at low doping. First, following a recent Gutzwiller-projected mean-field approach by one of us (Phys. Rev. B. {\bf 72}, 060508(R) (2005)), we investigate, as a function of doping and Coulomb repulsion, the stability of the staggered flux phase with respect to small spontaneous modulations of squared unit cells ranging from $2\times 2$ to $\sqrt{32}\times\sqrt{32}$. It is found that a $4\times 4$ bond-order (BO) modulation appears spontaneously on top of the staggered flux pattern for hole doping around 1/8. A related wave-function is then constructed and optimized accurately and its properties studied extensively using an approximation-free variational Monte Carlo scheme. Finally, the competition of the BO-modulated staggered flux wave-function w.r.t. the d-wave RVB wave-function or the commensurate flux state is investigated. It is found that a short range Coulomb repulsion penalizes the d-wave superconductor and that a moderate Coulomb repulsion brings them very close in energy. Our results are discussed in connection to the STM observations in the under-doped regime of some cuprates.Comment: 10 pages, 9 figure

Asymmetric spin-1/2 two-leg ladders

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and \kappa J_|| along legs (\kappa <= 1) and ferromagnetic rung coupling, J_\perp. This model is characterized by a gap \Delta in the spectrum of spin excitations. We show that in the large J_\perp limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at \kappa=1, admits a linear scaling for the spin gap \Delta ~ J_\perp. The second class appears for a strong asymmetry of the coupling along legs, \kappa J_|| << J_\perp << J_|| and is characterized by two energy scales: the exponentially small spin gap \Delta ~ J_\perp \exp(-J_|| / J_\perp), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ~ J_\perp^2 /J_|| . We report numerical results obtained by exact diagonalization, density matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetry. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.Comment: 18 pages, 11 figure

Combined analytical and numerical approach to study magnetization plateaux in doped quasi-one-dimensional antiferromagnets

We investigate the magnetic properties of quasi-one-dimensional quantum spin-S antiferromagnets. We use a combination of analytical and numerical techniques to study the presence of plateaux in the magnetization curve. The analytical technique consists in a path integral formulation in terms of coherent states. This technique can be extended to the presence of doping and has the advantage of a much better control for large spins than the usual bosonization technique. We discuss the appearance of doping-dependent plateaux in the magnetization curves for spin-S chains and ladders. The analytical results are complemented by a density matrix renormalization group (DMRG) study for a trimerized spin-1/2 and anisotropic spin-3/2 doped chains.Comment: 12 pages, 5 figure

Connectivity for the frisbee architecture

In this paper we investigate the kconnectivity threshold of distributed dense ad hoc heterogeneous wireless sensor network architecture. We consider the situation when sensors are deployed in the surveillance area according to a uniform distribution perturbed by a Gaussian noise. We derive analytically the minimum detection range which guarantees an emerging structure in the network, namely the connectivity, which becomes larger and larger as the number of sensors in the network increase. This allows the target track to be propagated almost surely throughout the network using the minimum possible amount ofprime energy. We report the results of some simulation experiments which further support the theoretical results

Algorithms for the selection of the active sensors in distributed tracking: Comparison between Frisbee and GNS methods

This paper compares two different approaches for sensor selection for distributed tracking: 1) The Frisbee method, and 2) Global Node Selection (GNS). The Frisbee method is based on the proximity of the nodes to the predicted location of the target; GNS is based on minimizing the unbiased Cramer Rao lower bound (CRLB). Both theoretical and experimental results indicate that the Frisbee method is as effective as GNS. Furthermore, the Frisbee method is attractive due to its very light computational load

Antiferromagnetism and hole pair checkerboard in the vortex state of high Tc superconductors

We propose a microscopic state for the vortex phase of BSCO superconductors. Around the vortex core or above H_{c2}, the d wave hole pairs form a checkerboard localized in the commensurate antiferromagnetic background. We discuss this theory in connection with recent STM experiments.Comment: Final versio