Investigation of the [1,5]-hydride shift as a route to nitro-Mannich cyclisations

Conditions were found for the [1,5]-hydride shift nitro-Mannich reaction that led to the synthesis of 2,3-disubstituted tetrahydroquinolines. Two simple cyclic amine substrates gave diastereomerically pure rearranged products in 65 and 90% yields by refluxing in HFIP. A more general procedure used Gd(OTf)3 as a catalyst and successfully rearranged other cyclic and acyclic amines in 42–84% yield with diastereomeric ratios of 75:25 to >95:5 in favour of the anti-diastereoisomer (9 examples). Two examples of sulphur containing heterocycles gave lower yields of 9 and 25%. Electron withdrawing substituents were shown to have a deleterious effect on the success of the reaction. The results indicated the limitation of the [1,5]-hydride shift nitro-Mannich reaction with respect to the stability of the intermediate iminium ion

Instability of a Landau Fermi liquid as the Mott insulator is approached

We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the 4 points $(\pm \pi/2, \pm \pi/2)$ as the electron density is increased. Umklapp processes at the 4 patches near $(\pm \pi/2, \pm\pi/2)$ lead the renormalization group equations to scale to strong coupling resembling the behavior of a 2-leg ladder at half-filling. The incompressible character of the fixed point causes a breakdown of Landau theory at these patches. A further increase in density spreads the incompressible regions so that the open Fermi surface shrinks to 4 disconnected segments. This non-Landau state, in which parts of the Fermi surface are truncated to form an insulating spin liquid, has many features in common with phenomenological models recently proposed for the cuprate superconductors.Comment: Minor changes. LaTeX2e, 12 pages, 5 figures. J. Phys. CM 10 (1998) L38

Anisotropy of Magnetic Interactions in the Spin-Ladder Compound (C5_5H12_{12}N)2_2CuBr4_4

Magnetic excitations in the spin-ladder material (C$_5$H$_{12}$N)$_2$CuBr$_4$ [BPCB] are probed by high-resolution multi-frequency electron spin resonance (ESR) spectroscopy. Our experiments provide a direct evidence for a biaxial anisotropy ($\sim 5\%$ of the dominant exchange interaction), that is in contrast to a fully isotropic spin-ladder model employed for this system previously. It is argued that this anisotropy in BPCB is caused by spin-orbit coupling, which appears to be important for describing magnetic properties of this compound. The zero-field zone-center gap in the excitation spectrum of BPCB, $\Delta_0/k_{B}=16.5$ K, is detected directly. Furthermore, an ESR signature of the inter-ladder exchange interactions is obtained. The detailed characterization of the anisotropy in BPCB completes the determination of the full spin hamiltonian of this exceptional spin-ladder material and shows ways to study anisotropy effects in spin ladders.Comment: 6 pages, 6 figure

A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda| |\log T| \le K$ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.Comment: 4 pages, no figure

Numerical Jordan-Wigner approach for two dimensional spin systems

We present a numerical self consistent variational approach based on the Jordan-Wigner transformation for two dimensional spin systems. We apply it to the study of the well known quantum (S=1/2) antiferromagnetic XXZ system as a function of the easy-axis anisotropy \Delta on a periodic square lattice. For the SU(2) case the method converges to a N\'eel ordered ground state irrespectively of the input density profile used and in accordance with other studies. This shows the potential utility of the proposed method to investigate more complicated situations like frustrated or disordered systems.Comment: Revtex, 8 pages, 4 figure

Metal-insulator crossover in the Boson-Fermion model in infinite dimensions

The Boson-Fermion model, describing a mixture of tightly bound electron pairs and quasi-free electrons hybridized with each other via a charge exchange term, is studied in the limit of infinite dimensions, using the Non-Crossing Approximation within the Dynamical Mean Field Theory. It is shown that a metal-insulator crossover, driven by strong pair fluctuations, takes place as the temperature is lowered. It manifests itself in the opening of a pseudogap in the electron density of states, accompanied by a corresponding effect in the optical and dc conductivity.Comment: 4 pages, 3 figures, to be published in Phys. Rev. Let

High-Field ESR Measurements of S=1/2 Kagome Lattice Antiferromagnet BaCu3_3V2_2O8_8(OH)2_2

High-field electron spin resonance (ESR) measurements have been performed on vesignieite BaCu$_3$V$_2$O$_8$(OH)$_2$, which is considered as a nearly ideal model substance of $S$=1/2 kagome antiferromagnet, in the temperature region from 1.9 to 265 K. The frequency region is from 60 to 360 GHz and the applied pulsed magnetic field is up to 16 T. Observed g-value and linewidth show the increase below 20 K, which suggest the development of the short range order. Moreover, a gapless spin liquid ground state is suggested from the frequency-field relation at 1.9 K.Comment: 5 pages, 6 figures, jpsj2 class file, to be published in J. Phys. Soc. Jp

Measurements in two bases are sufficient for certifying high-dimensional entanglement

High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of high-dimensional entanglement. In particular, it is desirable to do so without resorting to inefficient full state tomography. Here, we show how carefully constructed measurements in two bases (one of which is not orthonormal) can be used to faithfully and efficiently certify bipartite high-dimensional states and their entanglement for any physical platform. To showcase the practicality of this approach under realistic conditions, we put it to the test for photons entangled in their orbital angular momentum. In our experimental setup, we are able to verify 9-dimensional entanglement for a pair of photons on a 11-dimensional subspace each, at present the highest amount certified without any assumptions on the state.Comment: 11+14 pages, 2+7 figure

Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization - asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases - a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M. Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and Experiment, Springer Proceedings in Physics 173. arXiv admin note: text overlap with arXiv:1405.112

Localization from quantum interference in one-dimensional disordered potentials

We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of the disordered potential. This is equivalent of assuming a phase randomization of the off-diagonal/interference terms. We demonstrate these results through numerical calculations of the dynamics of ultracold atoms in the one-dimensional speckle and quasiperiodic potentials used in the recent experiments that lead to the observation of Anderson localization for matter waves [Billy et al., Nature 453, 891 (2008); Roati et al., Nature 453, 895 (2008)]. For the quasiperiodic case, we also discuss the implications of using continuos or discrete models.Comment: 5 pages, 3 figures; minor changes, references update