arXiv subjects

Jaime Fabián Nieto Castellanos

Publications and source records attributed to Jaime Fabián Nieto Castellanos.

6 recordsLinked to original sources

arXiv2026

A first look at Structured-Multiscale Algebraic Multigrid for Lattice Field Theory

State-of-the-art solvers for the Dirac equation in Lattice QCD are based on adaptive multigrid methods. These require fine-tuning of many algorithmic parameters to achieve optimal performance. We apply a new multigrid approach to Lattice Field Theory adapted from oil-reservoir simulations: Structured-Multiscale Algebraic Multigrid (SM-AMG). This method builds compact aggregates with overlapping borders to coarsen the grid and yields accurate interpolation. A key advantage is that aggregate size is the primary tunable parameter. For our results, we used SM-AMG in an algebraic approach, called Aggregative-Multiscale AMG (AM-AMG). We benchmark the efficiency of AM-AMG against that of DD$α$AMG, a successful adaptive multigrid solver which alleviates critical slowing down. The two solvers are compared within the framework of the two-flavor Schwinger model using the Wilson discretization. On fine lattices, the operation count of both methods is similar near the critical point and for large volumes, reflecting a comparable computational cost. However, the number of fine-grid iterations is larger for AM-AMG. On coarse lattices, AM-AMG encounters difficulties to remove the low modes close to the critical mass.

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arXiv2023

A pion decay constant in the multi-flavor Schwinger model

The pion decay constant $F_π$ plays an important role in QCD and in Chiral Perturbation Theory. It is hardly known, however, that a corresponding constant exists in the Schwinger model with $N_{\rm f} \geq 2$ degenerate fermion flavors. In this case, the ``pion'' does not decay and $F_π$is dimensionless. Still, $F_π$ can be defined by 2d analogies to the Gell-Mann--Oakes--Renner relation, the Witten--Veneziano formula and the residual ``pion'' mass in the $δ$-regime. With suitable assumptions, and by inserting simulation data, these QCD-inspired relations are all compatible with $F_π \simeq 1/\sqrt{2π}$ at zero fermion mass, as we observe for $N_{\rm f} = 2, \dots , 6$. We conclude that this is a meaningful constant in the multi-flavor Schwinger model.

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arXiv2023

Non-equilibrium dynamics of topological defects in the 3d O(2) model

We present a study of the 3d O(2) non-linear $σ$-model on the lattice, which exhibits topological defects in the form of vortices. They tend to organize into vortex lines that bear close analogies with global cosmic strings. Therefore, this model serves as a testbed for studying the dynamics of topological defects. It undergoes a second order phase transition, hence it is appropriate for investigating the Kibble-Zurek mechanism. In this regard, we explore the persistence of topological defects when the temperature is rapidly reduced from above to below the critical temperature; this cooling (or "quenching") process takes the system out of equilibrium. We probe a wide range of inverse cooling rates $τ_{\rm Q}$ and final temperatures, employing distinct Monte Carlo algorithms. The results consistently show that the density of persisting topological defects follows a power-law in $τ_{\rm Q}$, in agreement with Zurek's conjecture. On the other hand, at this point our results do not confirm Zurek's prediction for the exponent in this power-law, but its final test is still under investigation.

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arXiv2023

An analogue to the pion decay constant in the multi-flavor Schwinger model

We study the Schwinger model with $N_{\rm f} \geq 2$ degenerate fermion flavors, by means of lattice simulations. We use dynamical Wilson fermions for $N_{\rm f} = 2$, and re-weighted quenched configurations for overlap-hypercube fermions with $N_{\rm f} \leq 6$. In this framework, we explore an analogue of the QCD pion decay constant $F_π$, which is dimensionless in $d=2$, and which has hardly been considered in the literature. We determine $F_π$ by three independent methods, with numerical and analytical ingredients. First, we consider the 2-dimensional version of the Gell-Mann--Oakes--Renner relation, where we insert both theoretical and numerical values for the quantities involved. Next we refer to the $δ$-regime, {\it i.e.\ a small spatial volume, where we assume formulae from Chiral Perturbation Theory to apply even in the absence of Nambu-Goldstone bosons. We further postulate an effective relation between $N_{\rm f}$ and the number of relevant, light bosons, which we denote as "pions". Thus $F_π$ is obtained from the residual "pion" mass in the chiral limit, which is a finite-size effect. Finally, we address to the 2-dimensional Witten--Veneziano formula: it yields a value for $F_η$, which we identify with $F_π$, as in large-$N_{\rm c}$ QCD. All three approaches consistently lead to $F_π \simeq 1/\sqrt{2 π}$ at fermion mass $m=0$, which implies that this quantity is meaningful.

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arXiv2022

New insight in the 2-flavor Schwinger model based on lattice simulations

We consider the Schwinger model with two degenerate, light fermion flavors by means of lattice simulations. At finite temperature, we probe the viability of a bosonization method by Hosotani et al. Next we explore an analogue to the pion decay constant, which agrees for independent formulations based on the Gell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula and the $δ$-regime. Finally we confront several conjectures about the chiral condensate with lattice results.

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arXiv2021

Finite temperature and delta-regime in the 2-flavor Schwinger model

The Schwinger model is often used as a testbed for conceptual and numerical approaches in lattice field theory. Still, some of its rich physical properties in anisotropic volumes have not yet been explored. For the multi-flavor finite temperature Schwinger model there is an approximate solution by Hosotani et al. based on bosonization. We perform lattice simulations and check the validity of this approximation in the case of two flavors. Next we exchange the rôle of the coordinates to enter the $δ$-regime, and measure the dependence of the residual "pion" mass on the spatial size, at zero temperature. Our results show that universal features, which were derived by Leutwyler, Hasenfratz and Niedermayer referring to quasi-spontaneous symmetry breaking in $d>2$, extend even to $d=2$. This enables the computation of the Schwinger model counterpart of the pion decay constant $F_π$. It is consistent with an earlier determination by Harada et al. who considered the divergence of the axial current in a light-cone formulation, and with analytical results that we conjecture from 2d versions of the Witten--Veneziano formula and the Gell-Mann--Oakes--Renner relation, which suggest $F_π = 1/ \sqrt{2π}$.

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