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Claudio Bonanno

Publications and source records attributed to Claudio Bonanno.

At least 55 records · Page 3Linked to original sources
arXiv2024

Sphaleron rate of $N_f=2+1$ QCD

We compute the sphaleron rate of $N_f=2+1$ QCD at the physical point for a range of temperatures $200$ MeV $\lesssim T \lesssim 600$ MeV. We adopt a strategy recently applied in the quenched case, based on the extraction of the rate via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is finally computed by performing a continuum limit at fixed physical smoothing radius, followed by a zero-smoothing extrapolation. Dynamical fermions were discretized using the staggered formulation, which is known to yield large lattice artifacts for the topological susceptibility. However, we find them to be rather mild for the sphaleron rate.

hep-lat↗
arXiv2024

The topological susceptibility slope $χ^\prime$ of the pure-gauge SU(3) Yang-Mills theory

We determine the pure-gauge $\mathrm{SU}(3)$ topological susceptibility slope $χ^\prime$, related to the next-to-leading-order term of the momentum expansion of the topological charge density 2-point correlator, from numerical lattice Monte Carlo simulations. Our strategy consists in performing a double-limit extrapolation: first we take the continuum limit at fixed smoothing radius, then we take the zero-smoothing-radius limit. Our final result is $χ^\prime = [17.1(2.1)~\mathrm{MeV}]^2$. We also discuss a theoretical argument to predict its value in the large-$N$ limit, which turns out to be remarkably close to the obtained $N=3$ lattice result.

hep-lat↗
arXiv2023

Sphaleron rate as an inverse problem: a novel lattice approach

We compute the sphaleron rate on the lattice. We adopt a novel strategy based on the extraction of the spectral density via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is computed by performing controlled continuum limit and zero-smoothing extrapolations both in pure gauge and, for the first time, in full QCD.

hep-lat↗
arXiv2023

The Twisted Gradient Flow strong coupling with Parallel Tempering on Boundary Conditions

We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions (PTBC). The TGF is a gradient flow-based renormalization scheme formulated in an asymmetric lattice with twisted boundary conditions. Combined with step scaling, it has been successfully used to calculate the $\mathrm{SU}(3)$ $Λ$ parameter. As with all gradient flow-based schemes, the coupling constant is highly correlated with the topological charge and affected by topology freezing, an issue addressed by projecting the determination of the coupling onto the zero topological sector. As an alternative to the zero-charge projection, we combine TGF with PTBC, by replicating multiple copies of the same lattice, interpolating between periodic and open boundary conditions in a parallel-tempered manner. We present a first exploration of these ideas by analyzing specific ensembles of $\mathrm{SU}(3)$ lattices with and without PTBC.

hep-lat↗
arXiv2023

The large-$N$ limit of the chiral condensate from twisted reduced models

We compute the large-$N$ limit of the QCD chiral condensate on the lattice using twisted reduced models, and performing controlled continuum and chiral extrapolations. We perform two different calculations: one consists in extracting the chiral condensate from the quark mass dependence of the pion mass, and the other consists in extracting the chiral condensate from the behaviour of the mode number of the Wilson-Dirac operator for small eigenvalues. We find consistency between the results of the two methods, giving a joint estimate of $\lim_{N\to\infty}Σ(N)/N=[184(13)$ MeV$]^3$ ($\overline{\mathrm{MS}}$, $μ=2$ GeV, taking the square root of the string tension $\sqrtσ=440$ MeV to set the scale), in remarkable agreement with the $\mathrm{SU}(3)$ 2-flavor FLAG result.

hep-lat↗
arXiv2023

The chiral condensate at large $N$

We present results for the large-$N$ limit of the chiral condensate computed from twisted reduced models. We followed a two-fold strategy, one constiting in extracting the condensate from the quark-mass dependence of the pion mass, the other consisting in extracting the condensate from the mode number of the Dirac operator.

hep-lat↗
arXiv2023

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 $\mathrm{CP}^{N-1}$ 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.

hep-lat↗
arXiv2023

The chiral condensate of $N_f=2+1$ QCD from the spectrum of the staggered Dirac operator

We compute the chiral condensate of $2+1$ QCD from the mode number of the staggered Dirac operator, performing controlled extrapolations to both the continuum and the chiral limit. We consider also alternative strategies, based on the quark mass dependence of the topological susceptibility and of the pion mass, and obtain consistent results within errors. Results are also consistent with phenomenological expectations and with previous numerical determinations obtained with different lattice discretizations.

hep-lat↗
arXiv2023

Sphaleron rate from lattice QCD

We compute the sphaleron rate on the lattice from the inversion of the Euclidean time correlators of the topological charge density, performing also controlled continuum and zero-smoothing extrapolations. The correlator inversion is performed by means of a recently-proposed modification of the Backus-Gilbert method.

hep-lat↗
arXiv2023

Sphaleron rate from a modified Backus-Gilbert inversion method

We compute the sphaleron rate in quenched QCD for a temperature $T \simeq 1.24~T_c$ from the inversion of the Euclidean lattice time correlator of the topological charge density. We explore and compare two different strategies: one follows a new approach proposed in this study and consists in extracting the rate from finite lattice spacing correlators, and then in taking the continuum limit at fixed smoothing radius followed by a zero-smoothing extrapolation; the other follows the traditional approach of extracting the rate after performing such double extrapolation directly on the correlator. In both cases the rate is obtained from a recently-proposed modification of the standard Backus-Gilbert procedure. The two strategies lead to compatible estimates within errors, which are then compared to previous results in the literature at the same or similar temperatures; the new strategy permits to obtain improved results, in terms of statistical and systematic uncertainties.

hep-lat↗
arXiv2023

Quantum Algorithms for the computation of quantum thermal averages at work

Recently, a variety of quantum algorithms have been devised to estimate thermal averages on a genuine quantum processor. In this paper, we consider the practical implementation of the so-called Quantum-Quantum Metropolis algorithm. As a testbed for this purpose, we simulate a basic system of three frustrated quantum spins and discuss its systematics, also in comparison with the Quantum Metropolis Sampling algorithm.

quant-ph↗
arXiv2023

Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

hep-lat↗
arXiv2023

Benchmarking the Ising Universality Class in $3 \le d < 4$ dimensions

The Ising critical exponents $η$, $ν$ and $ω$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon-expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

hep-th↗
arXiv2023

On integer partitions and continued fraction type algorithms

We show that the additive-slow-Farey version of the traditional continued fractions algorithm has a natural interpretation as a method for producing integer partitions of a positive number $n$ into two smaller numbers, with multiplicity. We provide a complete description of how such integer partitions occur and of the conjugation for the corresponding Young shapes via the dynamics of the classical Farey tree. We use the dynamics of the Farey map to get a new formula for $p(2,n)$, the number of ways for partitioning $n$ into two smaller positive integers, with multiplicity. We then do the analogue using the additive-slow-Farey version of the Triangle map (a type of multi-dimensional continued fraction algorithm), giving us a method for producing integer partitions of a positive number $n$ into three smaller numbers, with multiplicity. However different aspects of this generalisations remain unclear.

math.NT↗
arXiv2023

Lattice determination of the topological susceptibility slope $χ^\prime$ of $2d~\mathrm{CP}^{N-1}$ models at large $N$

We compute the topological susceptibility slope $χ^\prime$, related to the second moment of the two-point correlator of the topological charge density, of $2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte Carlo simulations. Our strategy consists in performing a double limit: first, we take the continuum limit of $χ^\prime$ at fixed smoothing radius in physical units; then, we take the zero-smoothing-radius limit. Since the same strategy can also be applied to $4d$ gauge theories and full QCD, where $χ^\prime$ plays an intriguing theoretical and phenomenological role, this work constitutes a step towards the lattice investigation of this quantity in such models.

hep-lat↗
arXiv2023

Topological susceptibility of $2d~\mathrm{CP}^1$ or $\mathrm{O}(3)$ non-linear $σ$-model: is it divergent or not?

The topological susceptibility of $2d$ $\mathrm{CP}^{N-1}$ models is expected, based on perturbative computations, to develop a divergence in the limit $N \to 2$, where these models reduce to the well-known non-linear $\mathrm{O}(3)$ $σ$-model. The divergence is due to the dominance of instantons of arbitrarily small size and its detection by numerical lattice simulations is notoriously difficult, because it is logarithmic in the lattice spacing. We approach the problem from a different perspective, studying the behavior of the model when the volume is fixed in dimensionless lattice units, where perturbative predictions are turned into more easily checkable behaviors. After testing this strategy for $N = 3$ and $4$, we apply it to $N = 2$, adopting at the same time a multicanonic algorithm to overcome the problem of rare topological fluctuations on asymptotically small lattices. Our final results fully confirm, by means of purely non-perturbative methods, the divergence of the topological susceptibility of the $2d$ $\mathrm{CP}^1$ model.

hep-lat↗
arXiv2023

Internal-wave billiards in trapezoids and similar tables

We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the pretense that the boundary at any collision point is either horizontal or vertical (relative to a predetermined direction representing gravity). These systems are point particle approximations for the motion of internal gravity waves in closed containers, hence the name. For a class of tables similar to rectangular trapezoids, but with the slanted leg replaced by a general curve with downward concavity, we prove that the dynamics has only three asymptotic regimes: (1) there exist a global attractor and a global repellor, which are periodic and might coincide; (2) there exists a beam of periodic trajectories, whose boundary (if any) comprises an attractor and a repellor for all the other trajectories; (3) all trajectories are dense (that is, the system is minimal). Furthermore, in the prominent case where the table is an actual trapezoid, we study the sets in parameter space relative to the three regimes. We prove in particular that the set for (1) has positive measure (giving a rigorous proof of the existence of Arnol'd tongues for internal-wave billiards), whereas the sets for (2) and (3) are non-empty but have measure zero.

math.DS↗