Matrix Product States: Symmetries and Two-Body Hamiltonians

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.Comment: PDFLatex, 12 pages and 6 figure

Resonating valence bond states in the PEPS formalism

We study resonating valence bond (RVB) states in the Projected Entangled Pair States (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the four-fold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. We investigate this interpolation using numerical PEPS methods, studying the decay of correlation functions, the change of overlap, and the entanglement spectrum, none of which exhibits signs of a phase transition.Comment: 11+9 pages, 28 figures. v2: More numerical results, and a few minor improvements. v3: Accepted version (minor changes relative to v2), Journal-Ref adde

Single-copy entanglement in a gapped quantum spin chain

The single-copy entanglement of a given many-body system is defined [J. Eisert and M. Cramer, Phys. Rev. A. 72, 042112 (2005)] as the maximal entanglement deterministically distillable from a bipartition of a single specimen of that system. For critical (gapless) spin chains, it was recently shown that this is exactly half the von Neumann entropy [R. Orus, J. I. Latorre, J. Eisert, and M. Cramer, Phys. Rev. A 73, 060303(R) (2006)], itself defined as the entanglement distillable in the asymptotic limit: i.e. given an infinite number of copies of the system. It is an open question as to what the equivalent behaviour for gapped systems is. In this paper, I show that for the paradigmatic spin-S Affleck-Kennedy-Lieb-Tasaki chain (the archetypal gapped chain), the single-copy entanglement is equal to the von Neumann entropy: i.e. all the entanglement present may be distilled from a single specimen.Comment: Typos corrected; accepted for publication in Phys. Rev. Lett.; comments welcom

Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator (MPDO) valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in Journal of Mathematical Physic

Gapless Hamiltonians for the toric code using the PEPS formalism

We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of Projected Entangled Pair States (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians".Comment: 8 pages, 2 figure

Evidences of evanescent Bloch waves in Phononic Crystals

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects.Comment: 8 pages, 3 figure

Reactivity Effects in a Very-High-Temperature Pebble-Bed Reactor

The very-high-temperature reactor (VHTR) is one of the most promising and innovative designs selected by the Generation IV International Forum. Although previous papers have focused on the study and optimization of several parameter of a VHTR conceptual design, there is still much work needed to achieve the commercial introduction of this technology. The primary aim of this study is to obtain the reactivity effects of such parameters as the temperature of the fuel, moderator, and reflector, and the poisoning by 135Xe and 149Sm in the VHTR critically. To reach this goal, the widely-used MCNP6 code was employed in order to simulate the neutronics of the VHTR. The viability of the utilization of the MCNP6 code and the developed model for the study of the physics of the VHTR core was confirmed through the calculation and comparison with benchmarks provided by the IAEA. Based on the results of the temperature coefficients of reactivity obtained, a negative reactivity effect on the system of about 12 pcm/K was found, as is expected in all the nuclear fission reactors, while the combined effect of fission products 135Xe and 149Sm implies a negative reactivity of 3475 pcm

Short Communication: The potential of portable near infrared spectroscopy for assuring quality and authenticity in the food chain, using Iberian hams as an example

This communication assesses the use of a portable near infrared (NIR) instrument to measure quantitative (fatty acid profile) properties and qualitative (‘Premium’ and ‘Non-premium’) categories of individual Iberian pork carcasses at the slaughterhouse. Acorn-fed Iberian pigs have more unsaturated fats than pigs fed conventional compound feed. Recent advances in miniaturisation have led to a number of handheld NIR devices being developed, allowing processing decisions to be made earlier, significantly reducing time and costs. The most common methods used for assessing quality and authenticity of Iberian hams are analysis of the fatty acid composition of subcutaneous fat using gas chromatography and DNA analysis. In this study, NIR calibrations for fatty acids and classification as premium or non-premium ham, based on carcass fat measured in situ, were developed using a portable NIR spectrometer. The accuracy of the quantitative equations was evaluated through the standard error of cross validation or standard error of prediction of 0.84 for palmitic acid (C16:0), 0.94 for stearic acid (C18:0), 1.47 for oleic acid (C18:1) and 0.58 for linoleic acid (C18:2). Qualitative calibrations provided acceptable results, with up to 98% of samples (n = 234) correctly classified with probabilities ⩾0.9. Results indicated a portable NIR instrument has the potential to be used to measure quality and authenticity of Iberian pork carcasses