202 research outputs found

    ξ/ξ2nd\xi/\xi_{2nd} ratio as a tool to refine Effective Polyakov Loop models

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    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 ξ2nd\xi_{2nd}. The ratio ξ/ξ2nd\xi/\xi_{2nd} 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 ξ\xi and ξ2nd\xi_{2nd} 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 ξ/ξ2nd\xi/\xi_{2nd} in the confining phase of the (D=3+1D=3+1) SU(2)\mathrm{SU}(2) 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

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    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

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    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 CPN−1\mathrm{CP}^{N-1} 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

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    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

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    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

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    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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