Entanglement entropy in one-dimensional disordered interacting system: The role of localization

The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using density matrix renormalization group (DMRG). A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite size effects, is proposed. This is used to extract the localization length as function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations.Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letter

Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model

The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement entropy always scales linearly with the block size. However, besides this \emph{area law} contribution, we find a subleading logarithmic correction at the quantum critical point. This correction is discussed from the point of view of an underlying percolation transition, both at finite and at zero temperature.Comment: 4.3 pages, 4 figure

Violation of area-law scaling for the entanglement entropy in spin 1/2 chains

Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half chain. Our result is complementary to the known relation between non-translational invariant, nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure

Area law and vacuum reordering in harmonic networks

We review a number of ideas related to area law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory and quantum information. An explicit computation in arbitrary dimensions of the geometric entropy of the ground state of a discretized scalar free field theory shows the expected area law result. In this case, area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations. Furthermore, the explicit control on all the eigenvalues of the reduced density matrix allows for a verification of entropy loss along the renormalization group trajectory driven by the mass term. A further result of our computation shows that single-copy entanglement also obeys area law scaling, majorization relations and decreases along renormalization group flows.Comment: 15 pages, 6 figures; typos correcte

Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model

We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.Comment: 4 pages, 2 figures, published versio

Molecular evolution of aphids and their primary ( Buchnera sp.) and secondary endosymbionts: implications for the role of symbiosis in insect evolution.

Aphids maintain an obligate, endosymbiotic association with Buchnera sp., a bacterium closely related to Escherichia coli. Bacteria are housed in specialized cells of organ-like structures called bacteriomes in the hemocoel of the aphid and are maternally transmitted. Phylogenetic studies have shown that the association had a single origin, dated about 200-250 million years ago, and that host and endosymbiont lineages have evolved in parallel since then. However, the pattern of deepest branching within the aphid family remains unsolved, which thereby hampers tin appraisal of, for example, the role played by horizontal gene transfer in the early evolution of Buchnera. The main role of Buchnera in this association is the biosynthesis and provisioning of essential amino acids to its aphid host. Physiological and metabolic studies have recently substantiated such nutritional role. In addition, genetic studies of Buchnera from several aphids have shown additional modifications, such as strong genome reduction, high A+T content compared to free-living bacteria, differential evolutionary rates, a relative increase in the number of non-synonymous substitutions, and gene amplification mediated by plasmids. Symbiosis is an active process in insect evolution cis revealed by the intermediate values of the previous characteristics showed by secondary symbionts compared to free-living bacteria and Buchnera

The Effect of Fertiliser Treatment on the Development of Rangelands in Argentina

In Argentina grazing of rangelands may result in a decrease in winter gramineous species with an increase in summer weeds such as Cynodon dactylon. Lolium multiflorum is an important forage resource for grazing in the autumn, winter and spring. A delay in its emergence may occur because of summer weeds, which reduces the germination rate. The proportion of the seed bank as ryegrass allows the recovery of natural grassland and facilitates an increase in the productivity of livestock. The objective of this study was the evaluation of the impact of application of fertiliser in the short term on the relationship with botanical composition at different herbage availabilities

Suppression of grapevine powdery mildew (Uncinula necator) by acibenzolar-S-methyl

Research Not

Multi-party entanglement in graph states

Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multi-party quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multi-particle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimension, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphies.Comment: 22 pages, 15 figures, 2 tables, typos corrected (e.g. in measurement rules), references added/update

Universal geometric entanglement close to quantum phase transitions

Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product state at every step of the process? In this paper we give a quantitative answer to this question by providing first analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size $L \gg \xi$ diverges with the correlation length as $(c/12) \log{(\xi/\epsilon)}$ close to a quantum critical point with central charge $c$, where $\epsilon$ is a cut-off at short distances. Moreover, the situation at criticality is also discussed and an upper bound on the critical global geometric entanglement is provided in terms of a logarithmic function of $L$.Comment: 4 pages, 3 figure