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    Agricultural Finance, Crop Production/Industries,

    Efficient representation of fully many-body localized systems using tensor networks

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    We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of \ell contiguous sites. We argue this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.Comment: Version 2, 16 pages, 16 figures. Larger systems and greater efficienc

    Evaluation of Modification of the Upper Batavia Dam on the Fox River, Illinois

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    Progress Report, Federal Aid Project F-136-R Segment 6Report issued on: August 2004Submitted to Office of Water Resources, Illinois Department of Natural Resource

    Projected entangled-pair states can describe chiral topological states

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    We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free fermionic PEPS which show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians, and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version, Journal-Ref adde

    Lattice sites of ion-implanted Li in diamond

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    Published in: Appl. Phys. Lett. 66 (1995) 2733-2735 citations recorded in [Science Citation Index] Abstract: Radioactive Li ions were implanted into natural IIa diamonds at temperatures between 100 K and 900 K. Emission channelling patterns of a-particles emitted in the nuclear decay of 8Li (t1/2 = 838 ms) were measured and, from a comparison with calculated emission channelling and blocking effects from Monte Carlo simulations, the lattice sites taken up by the Li ions were quantitatively determined. A fraction of 40(5)% of the implanted Li ions were found to be located on tetrahedral interstitial lattice sites, and 17(5)% on substitutional sites. The fractions of implanted Li on the two lattice sites showed no change with temperature, indicating that Li diffusion does not take place within the time window of our measurements.

    Marine epibiosis. IV The periwinkle Littonna littorea lacks typical antifculing defences - why are some populations so little fouled?

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    Epibiosis on the shells of Littorina littorea (L.) varies between populations. While snails from the Helgoland intertidal zone (North Sea) rarely carry any epibionts, subtidal snails from the Kiel Bight (Baltic Sea) are frequently fouled. This study shows that L. littorea lacks typical anti-fouling defence adaptations such as mechanical, physical or chemical defences. Our enclosure experiments suggest that epibiosis on the shells is inversely correlated to L. littorea population density. At high densities snails frequently pass over one another and subsequent grazing, bulldozing and/or foot mucus secretion may contribute to the inhibition of epibionts. Consequently, the observed differences in shell epibiosis between the 2 L. littorea populations may to a large extent be explained by considerably higher L. littorea abundances in the Helgoland intertidal zone. Differences in habitat conditions probably play a secondary role. We suggest that the fouling inhibiting factors associated with high population density (mucus secretion, bulldozing, mutual grazing) are to be considered as a biological disturbance which effectively blocks recruitment by most potential colonizers