Alessandro Nada

A bstract: We study the profile of the flux tube in the SU(2) gauge model in (2 + 1) dimensions, with a particular attention to the so called “intrinsic width” which drives the exponential decay of the flux density at large transverse distances. This quantity is directly related to the confining mechanism which generates the flux tube: to test the properties of the latter we study a wide range of different values of lattice spacing, temperature and flux tube lengths and show that our data are precise enough to distinguish between different confining models. In particular we show that at high temperatures (just below the deconfinement transition) the data are perfectly described by an Ising-like effective model based on the Svetitsky-Yaffe mapping. At lower temperatures this approximation does not hold anymore. In this regime (which is the most interesting one from a physical point of view) we test several alternative proposals and show that the dual superconductor model is the one which better fits the data. However, this proposal is not fully satisfactory, because the values of the Ginzburg-Landau parameter extracted from the fits increase with the length of the flux tube, which is not a feature predicted by the model. This suggests that a more sophisticated model is needed to explain confinement in non-abelian gauge theories and, at the same time, that our data on the intrinsic width may be a powerful tool to benchmark these candidates.

A bstract: We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional SU(3) Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as 0 . 045 fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions.

We study the profile of the flux tube in the SU(2) gauge model in (2 + 1) dimensions, with a particular attention to the so called "intrinsic width" which drives the exponential decay of the flux density at large transverse distances and represents a new physical scale of the model. This quantity is directly related to the confining mechanism which generates the flux tube and can be used to test its properties. We study a wide range of different values of lattice spacing, temperature and flux tube lengths and show that our data are precise enough to distinguish between different confining models. In particular we show that at high temperatures (just below the deconfinement transition) the data are perfectly described by an Ising-like effective model based on the Svetitsky-Yaffe mapping. At lower temperatures this approximation does not hold anymore. In this regime (which is the most interesting one from a physical point of view) we test several alternative proposals and show that the dual superconductor model is the one which better fits the data. However, this proposal is not fully satisfactory, because the values of the Ginzburg-Landau parameter extracted from the fits increase with the length of the flux tube, which is not a feature predicted by the model. This suggests that a more sophisticated model is needed to explain confinement in non-abelian gauge theories and, at the same time, that our data on the intrinsic width may be a powerful tool to benchmark these candidates.

O(N) vector models in three dimensions, when defined in a geometry with a compact direction and tuned to criticality, exhibit long-range fluctuations which induce a Casimir effect. The strength of the resulting interaction is encoded in the excess free-energy density, which depends on a universal coefficient: the Casimir amplitude. We present a high-precision numerical calculation of the latter by means of a nonequilibrium Monte Carlo algorithm and compare our findings with results obtained from large-N expansions and from the conformal bootstrap.

Nonequilibrium Markov chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski’s equality to sample from a target probability distribution. By driving a base probability distribution out of equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called stochastic normalizing flows (SNFs). In this work we present the first implementation of SNFs for SU(3) lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times. Published by the American Physical Society 2025

We introduce a novel technique to numerically calculate Rényi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the ϕ^{4} scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.

Flow-based architectures have recently proved to be an efficient tool for numerical simulations of Effective String Theories regularized on the lattice that otherwise cannot be efficiently sampled by standard Monte Carlo methods. In this work we use Stochastic Normalizing Flows, a state-of-the-art deep learning architecture based on non-equilibrium Monte Carlo simulations, to study different effective string models. After testing the reliability of this approach through a comparison with exact results for the Nambu-Gotō model, we discuss results on observables that are challenging to study analytically, such as the width of the string and the shape of the flux density. Furthermore, we perform a novel numerical study of Effective String Theories with terms beyond the Nambu-Gotō action, including a broader discussion on their significance for lattice gauge theories. The combination of these findings enables a quantitative description of the fine details of the confinement mechanism in different lattice gauge theories. The results presented in this work establish the reliability and feasibility of flow-based samplers for Effective String Theories and pave the way for future applications on more complex models.

We study the shape of the flux tube in lattice Yang-Mills theories and in particular its intrinsic width. In the framework of the Effective String Theory description of the confining flux tube this intrinsic width has no measurable effects on the inter-quark static potential, but it can be precisely detected looking at the profile of the flux tube. We address this problem with a set of high precision simulations in the (2+1) dimensional SU(2) model. We find two different behaviours as a function of the temperature. In the low temperature regime ($T \ll T_c$) we find a good agreement with an expression inspired by the dual superconductive model of confinement. In the high temperature regime ($T \lesssim T_c$) our data agree with a model based on the Svetitsky-Yaffe mapping. All our data in this regime can be described in terms of only one length scale, the intrinsic width, which turns out to be the same scale appearing in the confining inter-quark static potential.

Non-equilibrium Monte Carlo simulations based on Jarzynski's equality are a well-understood method to compute differences in free energy and also to sample from a target probability distribution without the need to thermalize the system under study. In each evolution, the system starts from a given base distribution at equilibrium and it is gradually driven out-of-equilibrium while evolving towards the target parameters. If the target distribution suffers from long autocorrelation times, this approach represents a promising candidate to mitigate critical slowing down. Out-of-equilibrium evolutions are conceptually similar to Normalizing Flows and they can be combined into a recently-developed architecture called Stochastic Normalizing Flows (SNFs). In this contribution we first focus on the promising scaling with the volume guaranteed by the purely stochastic approach in the SU(3) lattice gauge theory in 4 dimensions; then, we define an SNF by introducing gauge-equivariant layers between the out-of-equilibrium Monte Carlo updates, and we analyse the improvement obtained as well as the inherited scaling with the volume. Finally, we discuss how this approach can be systematically improved and how simulations of lattice gauge theories in four dimensions for large volumes and close to criticality can be realistically achieved.