491,628 research outputs found
Simulating Ising Spin Glasses on a Quantum Computer
A linear-time algorithm is presented for the construction of the Gibbs
distribution of configurations in the Ising model, on a quantum computer. The
algorithm is designed so that each run provides one configuration with a
quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be A linear-time algorithm is presented for the construction of
the Gibbs distribution of configurations in the Ising model, on a quantum
computer. The algorithm is designed so that each run provides one configuration
with a quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be applied in any dimension, to a class of spin-glass Ising
models with a finite portion of frustrated plaquettes, diluted Ising models,
and models with a magnetic field. applied in any dimension, to a class of
spin-glass Ising models with a finite portion of frustrated plaquettes, diluted
Ising models, and models with a magnetic field.Comment: 24 pages, 3 epsf figures, replaced with published and significantly
revised version. More info available at http://www.fh.huji.ac.il/~dani/ and
http://www.fiz.huji.ac.il/staff/acc/faculty/biha
The Construction of Mirror Symmetry
The construction of mirror symmetry in the heterotic string is reviewed in
the context of Calabi-Yau and Landau-Ginzburg compactifications. This framework
has the virtue of providing a large subspace of the configuration space of the
heterotic string, probing its structure far beyond the present reaches of
solvable models. The construction proceeds in two stages: First all
singularities/catastrophes which lead to ground states of the heterotic string
are found. It is then shown that not all ground states described in this way
are independent but that certain classes of these LG/CY string vacua can be
related to other, simpler, theories via a process involving fractional
transformations of the order parameters as well as orbifolding. This
construction has far reaching consequences. Firstly it allows for a systematic
identification of mirror pairs that appear abundantly in this class of string
vacua, thereby showing that the emerging mirror symmetry is not accidental.
This is important because models with mirror flipped spectra are a priori
independent theories, described by distinct CY/LG models. It also shows that
mirror symmetry is not restricted to the space of string vacua described by
theories based on Fermat potentials (corresponding to minimal tensor models).
Furthermore it shows the need for a better set of coordinates of the
configuration space or else the structure of this space will remain obscure.
While the space of LG vacua is {\it not} completely mirror symmetric, results
described in the last part suggest that the space of Landau--Ginburg {\it
orbifolds} possesses this symmetry.Comment: 58 pages, Latex file, HD-THEP-92-1
Matrix Models and D-branes in Twistor String Theory
We construct two matrix models from twistor string theory: one by dimensional
reduction onto a rational curve and another one by introducing noncommutative
coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment
on the interpretation of our matrix models in terms of topological D-branes and
relate them to a recently proposed string field theory. By extending one of the
models, we can carry over all the ingredients of the super ADHM construction to
a D-brane configuration in the supertwistor space P^(3|4). Eventually, we
present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio
Quantum spin models with exact dimer ground states
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.
Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
The Hamiltonian symmetry reduction of the geodesics system on a symmetric
space of negative curvature by the maximal compact subgroup of the isometry
group is investigated at an arbitrary value of the momentum map. Restricting to
regular elements in the configuration space, the reduction generically yields a
spin Calogero model with hyperbolic interaction potentials defined by the root
system of the symmetric space. These models come equipped with Lax pairs and
many constants of motion, and can be integrated by the projection method. The
special values of the momentum map leading to spinless Calogero models are
classified under some conditions, explaining why the models with two
independent coupling constants are associated with as found by Olshanetsky and Perelomov. In the zero curvature limit our
models reproduce rational spin Calogero models studied previously and similar
models correspond to other (affine) symmetric spaces, too. The construction
works at the quantized level as well.Comment: 26 pages, v3: final version with a remark added after equation (5.3
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