679 research outputs found
Parallel software for lattice N=4 supersymmetric Yang--Mills theory
We present new parallel software, SUSY LATTICE, for lattice studies of
four-dimensional supersymmetric Yang--Mills theory with gauge
group SU(N). The lattice action is constructed to exactly preserve a single
supersymmetry charge at non-zero lattice spacing, up to additional potential
terms included to stabilize numerical simulations. The software evolved from
the MILC code for lattice QCD, and retains a similar large-scale framework
despite the different target theory. Many routines are adapted from an existing
serial code, which SUSY LATTICE supersedes. This paper provides an overview of
the new parallel software, summarizing the lattice system, describing the
applications that are currently provided and explaining their basic workflow
for non-experts in lattice gauge theory. We discuss the parallel performance of
the code, and highlight some notable aspects of the documentation for those
interested in contributing to its future development.Comment: Code available at https://github.com/daschaich/sus
Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems
In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich
continuous dynamics and yet can be studied using finite bisimulations.
The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors; see e.g. Brihaye et al (2004), Davoren (1999), Lafferriere et al (2000).
The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done by Korovina et al (2004) where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained.
The bounds provide a basis for designing efficient algorithms for computing
bisimulations, solving reachability and motion planning problems
The BFSS model on the lattice
We study the maximally supersymmetric BFSS model at finite temperature and
its bosonic relative. For the bosonic model in dimensions, we find that
it effectively reduces to a system of gauged Gaussian matrix models. The
effective model captures the low temperature regime of the model including one
of its two phase transitions. The mass becomes for large
, with the 'tHooft coupling. Simulations of the bosonic-BFSS model
with give , which is also the mass gap of
the Hamiltonian. We argue that there is no `sign' problem in the maximally
supersymmetric BFSS model and perform detailed simulations of several
observables finding excellent agreement with AdS/CFT predictions when
corrections are included.Comment: 23 pages, 11 figure
Lattice simulation with the Majorana positivity
While the sign problem of the Dirac fermion is conditioned by the
semi-positivity of a determinant, that of the Majorana fermion is conditioned
by the semi-positivity of a Pfaffian. We introduce one sufficient condition for
the semi-positivity of a Pfaffian. Based on the semi-positivity condition, we
study an effective model of the Majorana fermion. We also present the
application to the Dirac fermionComment: Talk given at 35th annual International Symposium on Lattice Field
Theory (Lattice2017
A factorization algorithm to compute Pfaffians
We describe an explicit algorithm to factorize an even antisymmetric N^2
matrix into triangular and trivial factors. This allows for a straight forward
computation of Pfaffians (including their signs) at the cost of N^3/3 flops.Comment: 6 pages, 1 figure, V2: Minor changes in the text and refs. added, to
appear in CP
Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
We study ground states and elementary excitations of a system of bosonic
atoms and diatomic Feshbach molecules trapped in a one-dimensional optical
lattice using exact diagonalization and variational Monte Carlo methods. We
primarily study the case of an average filling of one boson per site. In
agreement with bosonization theory, we show that the ground state of the system
in the thermodynamic limit corresponds to the Pfaffian-like state when the
system is tuned towards the superfluid-to-Mott insulator quantum phase
transition. Our study clarifies the possibility of the creation of exotic
Pfaffian-like states in realistic one-dimensional systems. We also present
preliminary evidence that such states support non-Abelian anyonic excitations
that have potential application for fault-tolerant topological quantum
computation.Comment: 10 pages, 10 figures. Matching the version published Phys.Rev.
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