1,995 research outputs found
Towards the compression of parton densities through machine learning algorithms
One of the most fascinating challenges in the context of parton density
function (PDF) is the determination of the best combined PDF uncertainty from
individual PDF sets. Since 2014 multiple methodologies have been developed to
achieve this goal. In this proceedings we first summarize the strategy adopted
by the PDF4LHC15 recommendation and then, we discuss about a new approach to
Monte Carlo PDF compression based on clustering through machine learning
algorithms.Comment: 4 pages, 4 figures, to appear in the proceedings of 50th Rencontres
de Moriond, QCD and High Energy Interactions, La Thuile, Italy, March 201
A proof of the irreversibility of renormalization group flows in four dimensions
We present a proof of the irreversibility of renormalization group flows,
i.e. the c-theorem for unitary, renormalizable theories in four (or generally
even) dimensions. Using Ward identities for scale transformations and spectral
representation arguments, we show that the c-function based on the trace of the
energy-momentum tensor (originally suggested by Cardy) decreases monotonically
along renormalization group trajectories. At fixed points this c-function is
stationary and coincides with the coefficient of the Euler density in the trace
anomaly, while away from fixed points its decrease is due to the decoupling of
positive--norm massive modes.Comment: 22 pages, 2 figures, plain tex with harvmac and epsf; several typos
corrected; final version, to be published in Nucl. Phys.
Finite-size scaling exponents and entanglement in the two-level BCS model
We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio
Matrix Product States Algorithms and Continuous Systems
A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio
- …