2,135 research outputs found
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 . 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
- …