Bounds on universal quantum computation with perturbed 2d cluster states

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.Comment: 7 pages, 4 figures, revised version, to appear in PR

Trends in the magnetic properties of Fe, Co and Ni clusters and monolayers on Ir(111), Pt(111) and Au(111)

We present a detailed theoretical investigation on the magnetic properties of small single-layered Fe, Co and Ni clusters deposited on Ir(111), Pt(111) and Au(111). For this a fully relativistic {\em ab-initio} scheme based on density functional theory has been used. We analyse the element, size and geometry specific variations of the atomic magnetic moments and their mutual exchange interactions as well as the magnetic anisotropy energy in these systems. Our results show that the atomic spin magnetic moments in the Fe and Co clusters decrease almost linearly with coordination on all three substrates, while the corresponding orbital magnetic moments appear to be much more sensitive to the local atomic environment. The isotropic exchange interaction among the cluster atoms is always very strong for Fe and Co exceeding the values for bulk bcc Fe and hcp Co, whereas the anisotropic Dzyaloshinski-Moriya interaction is in general one or two orders of magnitude smaller when compared to the isotropic one. For the magnetic properties of Ni clusters the magnetic properties can show quite a different behaviour and we find in this case a strong tendency towards noncollinear magnetism

Effect of chemical disorder on NiMnSb investigated by Appearance Potential Spectroscopy: a theoretical study

The half-Heusler alloy NiMnSb is one of the local-moment ferromagnets with unique properties for future applications. Band structure calculations predict exclusively majority bands at the Fermi level, thus indicating {100%} spin polarization there. As one thinks about applications and the design of functional materials, the influence of chemical disorder in these materials must be considered. The magnetization, spin polarization, and electronic structure are expected to be sensitive to structural and stoichiometric changes. In this contribution, we report on an investigation of the spin-dependent electronic structure of NiMnSb. We studied the influence of chemical disorder on the unoccupied electronic density of states by use of the ab-initio Coherent Potential Approximation method. The theoretical analysis is discussed along with corresponding spin-resolved Appearance Potential Spectroscopy measurements. Our theoretical approach describes the spectra as the fully-relativistic self-convolution of the matrix-element weighted, orbitally resolved density of states.Comment: JPD submitte

Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.Comment: 19 page

A review of data on abundance, trends in abundance, habitat use and diet of ice-breeding seals in the Southern Ocean

The development of models of marine ecosystems in the Southern Ocean is becoming increasingly important as a means of understanding and managing impacts such as exploitation and climate change. Collating data from disparate sources, and understanding biases or uncertainties inherent in those data, are important first steps for improving ecosystem models. This review focuses on seals that breed in ice habitats of the Southern Ocean (i.e. crabeater seal, Lobodon carcinophaga; Ross seal, Ommatophoca rossii; leopard seal, Hydrurga leptonyx; and Weddell seal, Leptonychotes weddellii). Data on populations (abundance and trends in abundance), distribution and habitat use (movement, key habitat and environmental features) and foraging (diet) are summarised, and potential biases and uncertainties inherent in those data are identified and discussed. Spatial and temporal gaps in knowledge of the populations, habitats and diet of each species are also identified

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette