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

A New Lithospheric Density and Magnetic Susceptibility Model of Iran, Starting From High‐Resolution Seismic Tomography

We propose a new model for the crust and upper mantle in Iran by joint inversion of gravity and magnetic fields, constrained with a seismic tomography model. We then calculate shear modulus from the Vs velocities and densities. The crust and mantle tomography model is first converted to a density cube through empirical and petrological velocity-density relations. The starting susceptibility is assigned to a two-layer homogeneous model, above a heat flow-derived Curie depth. Considering the uncertainties in the density-velocity relations, and the starting layered susceptibility variation, we refine the model by a constrained inversion of the gravity and magnetic fields with a Bayesian approach, producing the final 3D density and susceptibility model. The area is tectonically active with high seismicity and active faulting which are regulated by the crustal density and rigidity variations. Higher rigidity matches lower seismicity and extended deserts and basins, suggesting the control of their development. The Neo-Tethys suture, extending similar to 1,500 km long, as well as the Paleo-Tethys suture match crustal scale density variations, defining characteristics of the lighter Arabian plate and denser Eurasian crust. The South Caspian Basin is enigmatic, due to focusing on the seismicity along all its borders, but with relatively low average rigidity, which is contrary to what is observed for Iran, where the reduced rigidity correlates with higher seismicity. The 3D density model will be useful for numerical geodynamic models and obtaining geologic inferences from the crustal-scale units. The inversion of potential fields may produce inconsistent results, since there are always multiple models that resolve the anomalies, and the use of other geophysical data sets is necessary. To resolve the problem, we extract information from a high-resolution seismic tomography. With seismic velocities and defining the different layers of the model, using data available in the literature, we realize an a-priori model, on which we perform a Bayesian joint gravity and magnetic inversion, to obtain a final 3D model of the Iranian lithosphere, with a detailed distribution of densities and susceptibilities. With density and velocity values, we also calculate the rigidity of the area. We then compare the models obtained, with geological and tectonic information of the area, observing how density and susceptibility distribution reproduce the position of the magmatic outcrops and the principal tectonic lineaments, indicating the position of the Neo-Tethyan and Paleo-Tethyan sutures. Also, the rigidity model is consistent with the seismicity distribution of the area. 3D Bayesian joint inversion builds a reliable model of the lithosphere in the Iranian collision belt, useful for rheological calculationsMost of the magmatic and tectonic features can be followed by density variations in the crust, partly extending to the lower crustJointly with the seismic Vs tomography, rigidity is obtained which explains the inhomogeneous distribution of seismicity in the are

Leak-Induced Pressure Decay During Transients in Viscoelastic Pipes. Preliminary Results

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Leak Detection in a Real Transmission Main Through Transient Tests: Deeds and Misdeeds

AbstractThis paper concerns the use of Transient Test‐Based Techniques (TTBTs) for fault detection in a long transmission main. It reports the results of two series of transient tests executed in a real and operating pipe system. Because of the complexity of the investigated pipeline that includes several stubs, different pressure wave generators were used at both the end sections. Precisely, transients were caused by a pump shut‐down and the Portable Pressure Wave Maker device. The analysis of the results shows that, according to the characteristics of the transient tests and the investigated system, only a part of the system can be explored properly from a given generation point. The proposed test procedure allows overcoming the negative effect of a change in the initial and boundary conditions. In fact, contrary to laboratory, in a real system, it is quite impossible to repeat tests in the same flow conditions. The success of the survey—with two leaks detected with a good precision—confirms the potential of the TTBTs for fault detection in real systems