1,594 research outputs found
Ground state and excitation spectra of a strongly correlated lattice by the coupled cluster method
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 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
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 -dimensional symmetric informationally complete
POVMs.Comment: A. T. and D. R. contributed equally for this projec
Polarisation of Graded Bundles
We construct the full linearisation functor which takes a graded bundle of
degree (a particular kind of graded manifold) and produces a -fold
vector bundle. We fully characterise the image of the full linearisation
functor and show that we obtain a subcategory of -fold vector bundles
consisting of symmetric -fold vector bundles equipped with a family of
morphisms indexed by the symmetric group . 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 -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
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
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
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
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