Improved cooling algorithm for gauge theories

We propose and study a ``gold-washing" - type of algorithm which smooths out the short range fluctuations but leaves invariant instantons above a certain size. The algorithm needs no monitoring or calibration.Comment: Latex file, 4 pages, 4 figures in uuencoded compressed tar file. Contribution to Lattice 9

Gauge invariant structures and Confinement

By looking at cooled configurations on the lattice, we study the presence of peaks in the action density, or its electric and magnetic components, in the SU(2) gauge vacuum. The peaks are seen to be of instanton-like nature and their number variation takes care of the drop in the string tension observed when cooling. Possible explanations of this finding are analysed.Comment: uuencoded and compressed file of the Postcript file newpaper.ps, fig1.ps,fig2.eps,fig3.ps and fig4.ps. 13 pages of text and 4 figures Style modifications and misprints correcte

A Monte Carlo study of old, new and tadpole improved actions

Scaling of mass ratios in intermediate volumes, obtained with improved SU(2) lattice actions is tested against analytic results for the Wilson and continuum action. A new improved action is introduced by adding a 2X2 plaquette to the Symanzik action. Completing a square leads to a covariant propagator that simplifies perturbative calculations. Data is presented on lattices of size 4**3X128, with lattice spacings of approximately 0.02 and 0.12 fermi. For the latter case no further improvement as compared to the tree-level action was observed when including the Lepage-Mackenzie tadpole correction to the one-loop improved Luscher-Weisz Symanzik action.Comment: 12 pages, including 2 tables and 2 figures, late

Bell inequalities from multilinear contractions

We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct consequence of non-vanishing commutators. The approach is motivated by generalizing recent work on non-linear inequalities which was based on the moduli of complex numbers, quaternions and octonions. We extend results on Peres conjecture about the validity of Bell inequalities for quantum states with positive partial transposes. Moreover, we show the possibility of obtaining unbounded quantum violations albeit we also prove that quantum mechanics can only violate the derived inequalities if three or more parties are involved.Comment: Published versio

Sequentially generated states for the study of two dimensional systems

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.Comment: 10 pages, 4 figure

Frustration free gapless Hamiltonians for Matrix Product States

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is $\R^+$. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit.Comment: 36 pages, new version with some contents rearranged, and a correction in the injective cas

Quantum Capacities of Bosonic Channels

We investigate the capacity of bosonic quantum channels for the transmission of quantum information. Achievable rates are determined from measurable moments of the channel by showing that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. Along the way we provide a complete characterization of degradable Gaussian channels and those arising from teleportation protocols.Comment: 5 pages, 2 figure

Improved action and Hamiltonian in finite volumes

We introduce a new Symanzik improved action by adding a 2x2 plaquette in such a way that the Feynman rules in the covariant gauge simplify. We call this the square Symanzik action. Some comparisons with the continuum and the standard Wilson action are made in intermediate volumes, where mass ratios are accurately known and the precise amount of improvement can be determined. Ratios of the Lambda parameters will be presented, as well as partial results for the one-loop improvement coefficients. We discuss some of the intricacies that arise because of violations of unitarity at the scale of the cutoff. In particular we show how a field redefinition in the zero-momentum effective action allows one to remove scaling violations linear in the lattice spacing.Comment: 6 pages, 2 figures. Talk presented at LATTICE96(improvement

Gapless Hamiltonians for the toric code using the PEPS formalism

We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of Projected Entangled Pair States (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians".Comment: 8 pages, 2 figure