202 research outputs found
ratio as a tool to refine Effective Polyakov Loop models
Effective Polyakov line actions are a powerful tool to study the finite
temperature behaviour of lattice gauge theories. They are much simpler to
simulate than the original lattice model and are affected by a milder sign
problem, but it is not clear to which extent they really capture the rich
spectrum of the original theories. We propose here a simple way to address this
issue based on the so called second moment correlation length . The
ratio between the exponential correlation length and the second
moment one is equal to 1 if only a single mass is present in the spectrum, and
it becomes larger and larger as the complexity of the spectrum increases. Since
both and are easy to measure on the lattice, this is a cheap
and efficient way to keep track of the spectrum of the theory. As an example of
the information one can obtain with this tool we study the behaviour of
in the confining phase of the () gauge
theory and show that it is compatible with 1 near the deconfinement transition,
but it increases dramatically as the temperature decreases. We also show that
this increase can be well understood in the framework of an effective string
description of the Polyakov loop correlator. This non-trivial behaviour should
be reproduced by the Polyakov loop effective action; thus, it represents a
stringent and challenging test of existing proposals and it may be used to
fine-tune the couplings and to identify the range of validity of the
approximations involved in their construction.Comment: 1+17 pages, 3 pdf figures; v2: 1+17 pages, 3 pdf figures: discussion
in section 1,2 and 5 expanded, misprints corrected; matches journal versio
Frequency-splitting estimators of single-propagator traces
Single-propagator traces are the most elementary fermion Wick contractions
which occur in numerical lattice QCD, and are usually computed by introducing
random-noise estimators to profit from volume averaging. The additional
contribution to the variance induced by the random noise is typically orders of
magnitude larger than the one due to the gauge field. We propose a new family
of stochastic estimators of single-propagator traces built upon a frequency
splitting combined with a hopping expansion of the quark propagator, and test
their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending
on the fermion bilinear considered, the cost of computing these diagrams is
reduced by one to two orders of magnitude or more with respect to standard
random-noise estimators. As two concrete examples of physics applications, we
compute the disconnected contributions to correlation functions of two vector
currents in the isosinglet omega channel and to the hadronic vacuum
polarization relevant for the muon anomalous magnetic moment. In both cases,
estimators with variances dominated by the gauge noise are computed with a
modest numerical effort. Theory suggests large gains for disconnected three and
higher point correlation functions as well. The frequency-splitting estimators
and their split-even components are directly applicable to the newly proposed
multi-level integration in the presence of fermions.Comment: 26 pages, 8 figures, LaTe
Out-of-equilibrium simulations to fight topological freezing
Calculations of topological observables in lattice gauge theories with
traditional Monte Carlo algorithms have long been known to be a difficult task,
owing to the effects of long autocorrelations times. Several mitigation
strategies have been put forward, including the use of open boundary conditions
and methods such as parallel tempering. In this contribution we examine a new
approach based on out-of-equilibrium Monte Carlo simulations. Starting from
thermalized configurations with open boundary conditions on a line defect,
periodic boundary conditions are gradually switched on. A sampling of
topological observables is then shown to be possible with a specific
reweighting-like technique inspired by Jarzynski's equality. We discuss the
efficiency of this approach using results obtained for the 2-dimensional
models. Furthermore, we outline the implementation of our
proposal in the context of Stochastic Normalizing Flows, as they share the same
theoretical framework of the non-equilibrium transformations we perform, and
can be thought of as their generalization.Comment: 1+8 pages, 6 figures, contribution for the 40th International
Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th,
2023, Fermi National Accelerator Laborator
Sampling Nambu-Goto theory using Normalizing Flows
Effective String Theory (EST) is a non-perturbative framework used to
describe confinement in Yang-Mills theory through the modeling of the
interquark potential in terms of vibrating strings. An efficient numerical
method to simulate such theories where analytical studies are challenging is
still lacking. However, in recent years a new class of deep generative models
called Normalizing Flows (NFs) has been proposed to sample lattice field
theories more efficiently than traditional Monte Carlo methods. In this
contribution, we show a proof of concept of the application of NFs to EST
regularized on the lattice. Namely, we introduce Physics-Informed Stochastic
Normalizing Flows and we use them to sample the Nambu-Goto string action with
two goals: use the known analytical results of this theory as a benchmark and
demonstrate the efficiency of our method in obtaining new results of physical
interest and in particular in providing a numerical proof for a conjecture
regarding the width of the string.Comment: 7 pages, 3 figures, contribution for the 40th International Symposium
on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi
National Accelerator Laborator
The equation of state with non-equilibrium methods
Jarzynski’s equality provides an elegant and powerful tool to directly compute differences in free energy in Monte Carlo simulations and it can be readily extended to lattice gauge theories to compute a large set of physically interesting observables. In this talk we present a novel technique to determine the thermodynamics of stronglyinteracting matter based on this relation, which allows for a direct and efficient determination of the pressure using out-of-equilibrium Monte Carlo simulations on the lattice. We present results for the equation of state of the SU(3) Yang-Mills theory in the confined and deconfined phases. Finally, we briefly discuss the generalization of this method for theories with fermions, with particular focus on the equation of state of QCD
QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
A precise lattice determination of the equation of state in SU(3) Yang-Mills
theory is carried out by means of a simulation algorithm, based on Jarzynski's
theorem, that allows one to compute physical quantities in thermodynamic
equilibrium, by driving the field configurations of the system out of
equilibrium. The physical results and the computational efficiency of the
algorithm are compared with other state-of-the-art lattice calculations, and
the extension to full QCD with dynamical fermions and to other observables is
discussed.Comment: 1+23 pages, 5 pdf figures; v2: 1+32 pages, 7 pdf figures, discussion
expanded, version published in the journa
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