Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations.

Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way. Our work thereby exposes fundamental limitations to a full and unbiased understanding of quantum many-body systems using PEPS.

Shadows of anyons and the entanglement structure of topological phases.

The low-temperature dynamics of quantum systems are dominated by the low-energy eigenstates. For two-dimensional systems in particular, exotic phenomena such as topological order and anyon excitations can emerge. While a complete low-energy description of strongly correlated systems is hard to obtain, essential information about the elementary excitations is encoded in the eigenvalue structure of the quantum transfer matrix. Here we study the transfer matrix of topological quantum systems using the tensor network formalism and demonstrate that topological quantum order requires a particular type of 'symmetry breaking' for the fixed point subspace. We also relate physical anyon excitations to domain-wall excitations at the level of the transfer matrix. This formalism enables us to determine the structure of the topological sectors in two-dimensional gapped phases very efficiently, therefore opening novel avenues for studying fundamental questions related to anyon condensation and confinement.

Edge theories in projected entangled pair state models.

We analyze the low energy excitations of spin lattice systems in two dimensions at zero temperature within the framework of projected entangled pair state models. Perturbations in the bulk give rise to physical excitations located at the edge. We identify the corresponding degrees of freedom, give a procedure to derive the edge Hamiltonian, and illustrate that it can exhibit a rich phase diagram. For topological models, the edge Hamiltonian is constrained by the topological order in the bulk, which gives rise to one-dimensional edge models with unconventional properties; for instance, a topologically ordered bulk can protect a ferromagnetic Ising chain at the edge against spontaneous symmetry breaking.

Projected entangled-pair states can describe chiral topological states.

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 nontrivial 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 projected entangled-pair states that 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.

Validation of a food frequency questionnaire for women with osteoporosis.

The importance of nutrient intakes in osteoporosis prevention in treatment is widely recognized. The objective of the present study was to develop and validate a FFQ for women with osteoporosis. The questionnaire was composed of 60 items, separated into 10 groups. The relative validation was accomplished through comparison of the 3-Day Food Record (3DR) with the FFQ. The 3DR was applied to 30 elderly women with confirmed osteoporosis, and after 45 days the FFQ was administrated. Statistical analysis comprised the Kolmogorov-Smirnov, Student T test and Pearson correlation coefficient. The agreement between two methods was evaluated by the frequency of similar classification into quartiles, and by the Bland-Altman method. No significant differences between methods were observed for the mean evaluated nutrients, except for carbohydrate and magnesium. Pearson correlation coefficients were positive and statistically significant for all nutrients. The overall proportion of subjects classified in the same quartile by the two methods was on average 50.01% and in the opposite quartile 0.47%. For calcium intake, only 3% of subjects were classified in opposite extreme quartiles by the two methods. The Bland-Altman analysis demonstrated that the differences obtained by the two methods in each subject were well distributed around the mean of the difference, and the disagreement increases as the mean intake increases. These results indicates that the FFQ for elderly women with osteoporosis presented here is highly acceptable and is an accurate method that can be used in large-scale or clinical studies for evaluation of nutrient intakes in a similar population.

Nonlocal resources in the presence of superselection rules.

Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the superselection induced variance of the local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation, and mixed state entanglement.

Trapped antiprotons produced by cosmic rays in the Earth's magnetosphere.

The existence of significant fluxes of antiparticles in the Earth magnetosphere has been predicted on theoretical considerations in this article. These antiparticles (positrons or antiprotons) at several hundred kilometers of altitudes, we believe are not of direct extraterrestrial origin, but are the natural products of nuclear reactions of the high energy primary cosmic rays (CR) and trapped protons (TP) confined in the terrestrial radiation belt, with the constituents of terrestrial atmosphere. Extraterrestrial positrons and antiprotons born in nuclear reactions of the same CR particles passing through only 5-7 g/cm2 of interstellar matter, exhibit lower fluxes compared to the antiprotons born at hundreds of g/cm2 in the atmosphere, which when confined in the magnetic field of the Earth (in any other planet), get accumulated. We present the results of the computations of the antiproton fluxes at 10 MeV to several GeV energies due to CR particle interactions with the matter in the interstellar space, and also with the residual atmosphere at altitudes of approximately 1000 km over the Earth's surface. The estimates show that the magnetospheric antiproton fluxes are greater by two orders of magnitude compared to the extraterrestrial fluxes measured at energies <1-2 GeV.