7,497 research outputs found
Iterative structure of finite loop integrals
In this paper we develop further and refine the method of differential
equations for computing Feynman integrals. In particular, we show that an
additional iterative structure emerges for finite loop integrals. As a concrete
non-trivial example we study planar master integrals of light-by-light
scattering to three loops, and derive analytic results for all values of the
Mandelstam variables and and the mass . We start with a recent
proposal for defining a basis of loop integrals having uniform transcendental
weight properties and use this approach to compute all planar two-loop master
integrals in dimensional regularization. We then show how this approach can be
further simplified when computing finite loop integrals. This allows us to
discuss precisely the subset of integrals that are relevant to the problem. We
find that this leads to a block triangular structure of the differential
equations, where the blocks correspond to integrals of different weight. We
explain how this block triangular form is found in an algorithmic way. Another
advantage of working in four dimensions is that integrals of different loop
orders are interconnected and can be seamlessly discussed within the same
formalism. We use this method to compute all finite master integrals needed up
to three loops. Finally, we remark that all integrals have simple Mandelstam
representations.Comment: 26 pages plus appendices, 5 figure
Finite-temperature phase diagram of the Heisenberg-Kitaev model
We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev
model on the hexagonal lattice, which has been suggested to describe the
spin-orbital exchange of the effective spin-1/2 momenta in the Mott insulating
Iridate Na2IrO3. At zero-temperature this model exhibits magnetically ordered
states well beyond the isotropic Heisenberg limit as well as an extended
gapless spin liquid phase around the highly anisotropic Kitaev limit. Using a
pseudofermion functional renormalization group (RG) approach, we extract both
the Curie-Weiss scale and the critical ordering scale (for the magnetically
ordered states) from the RG flow of the magnetic susceptibility. The
Curie-Weiss scale switches sign -- indicating a transition of the dominant
exchange from antiferromagnetic to ferromagnetic -- deep in the magnetically
ordered regime. For the latter we find no significant frustration, i.e. a
substantial suppression of the ordering scale with regard to the Curie-Weiss
scale. We discuss our results in light of recent experimental susceptibility
measurements for Na2IrO3.Comment: 4+e pages, 5 figure
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
The classical Kepler problem, as well as its quantum mechanical version, the
Hydrogen atom, enjoy a well-known hidden symmetry, the conservation of the
Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there
a relativistic quantum field theory extension that preserves this symmetry? In
this Letter we show that the answer is positive: in the non-relativistic limit,
we identify the dual conformal symmetry of planar super
Yang-Mills with the well-known symmetries of the Hydrogen atom. We point out
that the dual conformal symmetry offers a novel way to compute the spectrum of
bound states of massive bosons in the theory. We perform nontrivial tests
of this setup at weak and strong coupling, and comment on the possible
extension to arbitrary values of the coupling.Comment: 4 pages, 3 figures. Clarifications added; published versio
How SU(2) Anyons are Z Parafermions
We consider the braid group representation which describes the non-abelian
braiding statistics of the spin 1/2 particle world lines of an SU(2)
Chern-Simons theory. Up to an abelian phase, this is the same as the
non-Abelian statistics of the elementary quasiparticles of the
Read-Rezayi quantum Hall state. We show that these braiding statistics are
identical to those of Z Parafermions
A R\'enyi entropy perspective on topological order in classical toric code models
Concepts of information theory are increasingly used to characterize
collective phenomena in condensed matter systems, such as the use of
entanglement entropies to identify emergent topological order in interacting
quantum many-body systems. Here we employ classical variants of these concepts,
in particular R\'enyi entropies and their associated mutual information, to
identify topological order in classical systems. Like for their quantum
counterparts, the presence of topological order can be identified in such
classical systems via a universal, subleading contribution to the prevalent
volume and boundary laws of the classical R\'enyi entropies. We demonstrate
that an additional subleading contribution generically arises for all
R\'enyi entropies with when driving the system towards a
phase transition, e.g. into a conventionally ordered phase. This additional
subleading term, which we dub connectivity contribution, tracks back to partial
subsystem ordering and is proportional to the number of connected parts in a
given bipartition. Notably, the Levin-Wen summation scheme -- typically used to
extract the topological contribution to the R\'enyi entropies -- does not fully
eliminate this additional connectivity contribution in this classical context.
This indicates that the distillation of topological order from R\'enyi
entropies requires an additional level of scrutiny to distinguish topological
from non-topological contributions. This is also the case for quantum
systems, for which we discuss which entropies are sensitive to these
connectivity contributions. We showcase these findings by extensive numerical
simulations of a classical variant of the toric code model, for which we study
the stability of topological order in the presence of a magnetic field and at
finite temperatures from a R\'enyi entropy perspective.Comment: 17 pages, 19 figure
Subleading Regge limit from a soft anomalous dimension
Wilson lines capture important features of scattering amplitudes, for example
soft effects relevant for infrared divergences, and the Regge limit. Beyond the
leading power approximation, corrections to the eikonal picture have to be
taken into account. In this paper, we study such corrections in a model of
massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit,
where the mass is generated through a Higgs mechanism. Using known three-loop
analytic expressions for the scattering amplitude, we find that the first power
suppressed term has a very simple form, equal to a single power law. We propose
that its exponent is governed by the anomalous dimension of a Wilson loop with
a scalar inserted at the cusp, and we provide perturbative evidence for this
proposal. We also analyze other limits of the amplitude and conjecture an exact
formula for a total cross-section at high energies.Comment: 19 pages, several appendices, many figure
Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
Motivated by the recent synthesis of the spin-1 A-site spinel NiRhO, we investigate the classical to quantum crossover of a
frustrated - Heisenberg model on the diamond lattice upon varying the
spin length . Applying a recently developed pseudospin functional
renormalization group (pf-FRG) approach for arbitrary spin- magnets, we find
that systems with reside in the classical regime where the
low-temperature physics is dominated by the formation of coplanar spirals and a
thermal (order-by-disorder) transition. For smaller local moments =1 or
=1/2 we find that the system evades a thermal ordering transition and forms
a quantum spiral spin liquid where the fluctuations are restricted to
characteristic momentum-space surfaces. For the tetragonal phase of
NiRhO, a modified -- exchange
model is found to favor a conventionally ordered N\'eel state (for arbitrary
spin ) even in the presence of a strong local single-ion spin anisotropy and
it requires additional sources of frustration to explain the experimentally
observed absence of a thermal ordering transition.Comment: 11 pages, 14 figure
Transformations of High-Level Synthesis Codes for High-Performance Computing
Specialized hardware architectures promise a major step in performance and
energy efficiency over the traditional load/store devices currently employed in
large scale computing systems. The adoption of high-level synthesis (HLS) from
languages such as C/C++ and OpenCL has greatly increased programmer
productivity when designing for such platforms. While this has enabled a wider
audience to target specialized hardware, the optimization principles known from
traditional software design are no longer sufficient to implement
high-performance codes. Fast and efficient codes for reconfigurable platforms
are thus still challenging to design. To alleviate this, we present a set of
optimizing transformations for HLS, targeting scalable and efficient
architectures for high-performance computing (HPC) applications. Our work
provides a toolbox for developers, where we systematically identify classes of
transformations, the characteristics of their effect on the HLS code and the
resulting hardware (e.g., increases data reuse or resource consumption), and
the objectives that each transformation can target (e.g., resolve interface
contention, or increase parallelism). We show how these can be used to
efficiently exploit pipelining, on-chip distributed fast memory, and on-chip
streaming dataflow, allowing for massively parallel architectures. To quantify
the effect of our transformations, we use them to optimize a set of
throughput-oriented FPGA kernels, demonstrating that our enhancements are
sufficient to scale up parallelism within the hardware constraints. With the
transformations covered, we hope to establish a common framework for
performance engineers, compiler developers, and hardware developers, to tap
into the performance potential offered by specialized hardware architectures
using HLS
- …