A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation

We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.Comment: 5 pages, 1 figure; v2 has a simplified lattice, an extended analysis of errors, and some additional references; v3 published versio

Production of tau tau jj final states at the LHC and the TauSpinner algorithm: the spin-2 case

The TauSpinner algorithm is a tool that allows to modify the physics model of the Monte Carlo generated samples due to the changed assumptions of event production dynamics, but without the need of re-generating events. With the help of weights $\tau$-lepton production or decay processes can be modified accordingly to a new physics model. In a recent paper a new version TauSpinner ver.2.0.0 has been presented which includes a provision for introducing non-standard states and couplings and study their effects in the vector-boson-fusion processes by exploiting the spin correlations of $\tau$-lepton pair decay products in processes where final states include also two hard jets. In the present paper we document how this can be achieved taking as an example the non-standard spin-2 state that couples to Standard Model particles and tree-level matrix elements with complete helicity information included for the parton-parton scattering amplitudes into a $\tau$-lepton pair and two outgoing partons. This implementation is prepared as the external (user provided) routine for the TauSpinner algorithm. It exploits amplitudes generated by MadGraph5 and adopted to the TauSpinner algorithm format. Consistency tests of the implemented matrix elements, reweighting algorithm and numerical results for observables sensitive to $\tau$ polarization are presented.Comment: 17 pages, 6 figures; version published in EPJ

Application of TauSpinner for studies on tau-lepton polarization and spin correlations in Z, W and H decays at LHC

The tau-lepton plays an important role in the physics program at LHC. Its spin can be used for separation of signal from background or in measuring properties of New Particles decaying to tau leptons. The TauSpinner package represents a tool to modify tau spin effects in any sample containing tau leptons. Generated events, featuring taus produced from intermediate state W, Z, H bosons can be used as an input. The information on the polarization and spin correlations is reconstructed from the kinematics of the tau lepton(s) (nutau in case of W-mediated processes) and tau decay products. By weights, attributed on the event-by-event basis, it enables numerical evaluation and/or modification of the spin effects. We review distributions to monitor spin effects in leptonic and hadronic tau decays with up to three pions, to provide benchmarks for validation of spin content of the event sample and to visualize the tau lepton spin polarization and correlation effects. The demonstration examples for use of TauSpinner libraries, are documented. New validation methods of such an approach are provided. Other topics, like TauSpinner systematic errors or sensitivity of experimental distributions to spin, are addressed in part only. This approach is of interest for implementation of spin effects in embedded tau lepton samples, where Z to mu mu events from data of muons are replaced by simulated tau leptons. Embedding is used at LHC for estimating Z to tau tau background to H to tau tau signatures.Comment: 1+41 pages, 5 figures in main text, multitude of figures in appendice

A Contribution to the Examination of the Oral Mucosa Membrane Bioimpedance

U namjeri da ustanove osnovne vrijednosti bioimpedancije na zdravoj oralnoj sluznici autori su u 19 zdravih osoba uz pomoć posebno prilagođenoga mjernog uređaja mjerili vrijednosti modula i faznoga kuta bioimpedancije u deset referentnih točaka u usnoj šupljini. Mjerenje je izvršeno na deset frekvencija kvazilogaritamski rasprostranjenih u rasponu od 30 Hz do 1 MHz. Mjerenje je u svakoj točki trajalo 30 sekundi. Izmjerene vrijednosti pokazale su uočljive sličnosti distribucije rezultata za skupine mjernih točaka. Autori zaključuju da je dovoljno mjeriti na sluznici dorzuma jezika, nepca i obraza kao reprezentativnim područjima, a vrijednosti za ostala teže dostupna područja bitno se ne razlikuju od predloženih točaka. Također ja utvrđeno da se na visokim i niskim frakvencijama rezultati mjerenja grupiraju te se predlaže da se raspon frekvencija suzi na 103 do 105 Hz.Asample of 19 healthy persons were tested by means of a specially adapted measuring device in order to obtain module values and bioimpedance phase angles in ten reference points distributed along the oral mucosa. The measurements were carried out at ten approximately logarithmic frequencies set out within the range of 30 Hz to 1 MHz. Each measurement lasted 30 seconds. The results showed significant similarities on the group distribution of measuring points. This lead to the conclusion that the relevant measuring points were at lingual dorsum mucosa, hard palate and buccal mucosa, whereas the values for other less accessible regions did not significantly differ from the former. It was also found that the measuring results were concentrated at low and high frequencies. Therefore, it is advisable to narrow down the measuring range to 103 - 105 Hz

Production of \uptau τ lepton pairs with high pTp_T p T jets at the LHC and the TauSpinner reweighting algorithm

The TauSpinner algorithm allows to modify the physics of the Monte Carlo generated samples due to the changed assumptions of event production dynamics, without re-generating events. To each event it attributes weights: the spin effects of tau-lepton production or decay, or the production mechanism are modified. There is no need to repeat the detector response simulation. We document the extension to 2 to 4 processes in which the matrix elements for the parton-parton scattering amplitudes into a tau-lepton pair and two outgoing partons are used. Tree-level matrix elements for the Standard Model processes, including the Higgs boson production are used. Automatically generated codes by MadGraph5 have been adapted. Tests of the matrix elements, reweighting algorithm and numerical results are presented. For averaged tau lepton polarisation, we perform comparison of 2 to 2 and 2 to 4 matrix elements used to calculate the spin weight in pp to tau tau j j events. We show, that for events with tau-lepton pair close to the Z-boson peak, the tau-lepton polarisation calculated using 2 to 4 matrix elements is very close to the one calculated using 2 to 2 Born process only. For the m_(tautau) masses above the Z-boson peak, the effect from including 2 to 4 matrix elements is also marginal, however when restricting into subprocesses qq,q bar q to tau tau j j only, it can lead to a 10% difference on the predicted tau-lepton polarisation. Choice of electroweak scheme can have significant impact. The modification of the electroweak or strong interaction can be performed with the re-weighting technique. TauSpinner v.2.0.0, allows to introduce non-standard couplings for the Higgs boson and study their effects in the vector-boson-fusion. The discussion is relegated to forthcoming publications.Comment: 33 pages 7 figure

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum J1XXZJ_{1}^{XXZ}--J2XXZJ_{2}^{XXZ} model on the square lattice

We study the zero-temperature phase diagram of the $J_{1}^{XXZ}$--$J_{2}^{XXZ}$ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ($J_1 \equiv 1$) and next-nearest-neighbour ($J_2 > 0$) bonds. Both bonds have the same $XXZ$-type anisotropy in spin space. The effects on the quasiclassical N\'{e}el-ordered and collinear stripe-ordered states of varying the anisotropy parameter $\Delta$ is investigated using the coupled cluster method carried out to high orders. By contrast with the spin-1/2 case studied previously, we predict no intermediate disordered phase between the N\'{e}el and collinear stripe phases, for any value of the frustration $J_2/J_1$, for either the $z$-aligned ($\Delta > 1$) or $xy$-planar-aligned ($0 \leq \Delta < 1$) states. The quantum phase transition is determined to be first-order for all values of $J_2/J_1$ and $\Delta$. The position of the phase boundary $J_{2}^{c}(\Delta)$ is determined accurately. It is observed to deviate most from its classical position $J_2^c = {1/2}$ (for all values of $\Delta > 0$) at the Heisenberg isotropic point ($\Delta = 1$), where $J_{2}^{c}(1) = 0.55 \pm 0.01$. By contrast, at the XY isotropic point ($\Delta = 0$), we find $J_{2}^{c}(0) = 0.50 \pm 0.01$. In the Ising limit ($\Delta \to \infty$) $J_2^c \to 0.5$ as expected.Comment: 20 pages, 5 figure

Polar catastrophe and electronic reconstructions at the LaAlO3/SrTiO3 interface: evidence from optical second harmonic generation

The so-called "polar catastrophe", a sudden electronic reconstruction taking place to compensate for the interfacial ionic polar discontinuity, is currently considered as a likely factor to explain the surprising conductivity of the interface between the insulators LaAlO3 and SrTiO3. We applied optical second harmonic generation, a technique that a priori can detect both mobile and localized interfacial electrons, to investigating the electronic polar reconstructions taking place at the interface. As the LaAlO3 film thickness is increased, we identify two abrupt electronic rearrangements: the first takes place at a thickness of 3 unit cells, in the insulating state; the second occurs at a thickness of 4-6 unit cells, i.e., just above the threshold for which the samples become conducting. Two possible physical scenarios behind these observations are proposed. The first is based on an electronic transfer into localized electronic states at the interface that acts as a precursor of the conductivity onset. In the second scenario, the signal variations are attributed to the strong ionic relaxations taking place in the LaAlO3 layer

Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100 \times 100$ sites.Comment: Submitted to Teoreticheskaya i Matematicheskaya Fizika (special issue dedicated to the 90th anniversary of Professor Sergei Vladimirovich Tyablikov