1,594 research outputs found

    Ground state and excitation spectra of a strongly correlated lattice by the coupled cluster method

    Full text link
    We apply Coupled Cluster Method to a strongly correlated lattice and develop the Spectral Coupled Cluster equations by finding an approximation to the resolvent operator, that gives the spectral response for an certain class of probe operators. We apply the method to a MnO2MnO_2 plane model with a parameters choice which corresponds to previous experimental works and which gives a non-nominal symmetry ground state. We show that this state can be observed using our Spectral Coupled Cluster Method by probing the Coupled Cluster solution obtained from the nominal reference state. In this case one observes a negative energy resonance which corresponds to the true ground state

    Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation

    Full text link
    We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimisation problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the non-projectiveness of high-dimensional measurements in a black-box scenario based on self-tests of dd-dimensional symmetric informationally complete POVMs.Comment: A. T. and D. R. contributed equally for this projec

    Polarisation of Graded Bundles

    Full text link
    We construct the full linearisation functor which takes a graded bundle of degree kk (a particular kind of graded manifold) and produces a kk-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of kk-fold vector bundles consisting of symmetric kk-fold vector bundles equipped with a family of morphisms indexed by the symmetric group Sk{\mathbb S}_k. Interestingly, for the degree 2 case this additional structure gives rise to the notion of a symplectical double vector bundle, which is the skew-symmetric analogue of a metric double vector bundle. We also discuss the related case of fully linearising NN-manifolds, and how one can use the full linearisation functor to "superise" a graded bundle

    On choice of preconditioner for minimum residual methods for nonsymmetric matrices

    Get PDF
    Existing convergence bounds for Krylov subspace methods such as GMRES for nonsymmetric linear systems give little mathematical guidance for the choice of preconditioner. Here, we establish a desirable mathematical property of a preconditioner which guarantees that convergence of a minimum residual method will essentially depend only on the eigenvalues of the preconditioned system, as is true in the symmetric case. Our theory covers only a subset of nonsymmetric coefficient matrices but computations indicate that it might be more generally applicable

    A staggered fermion chain with supersymmetry on open intervals

    Full text link
    A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlev\'e VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.Comment: 21 pages, no figures; v2: typos correcte

    Maximum energy sequential matrix diagonalisation for parahermitian matrices

    Get PDF
    Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step
    corecore