arXiv subjects

Francesco Di Renzo

Publications and source records attributed to Francesco Di Renzo.

At least 37 records · Page 2Linked to original sources

arXiv2022

Inverse Renormalization Group in Quantum Field Theory

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional $ϕ^{4}$ scalar field theory on sizes as small as $V=8^{2}$, we apply the inverse transformations to produce rescaled systems of size up to $V'=512^{2}$ which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

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arXiv2021

Thimble regularisation of YM fields: crunching a hard problem

Thimble regularisation of Yang Mills theories is still to a very large extent terra incognita. We discuss a couple of topics related to this big issue. 2d YM theories are in principle good candidates as a working ground. An analytic solution is known, for which one can switch from a solution in terms of a sum over characters to a form which is a sum over critical points. We would be interested in an explicit realisation of this mechanism in the lattice regularisation, which is actually quite hard to work out. A second topic is the inclusion of a topological term in the lattice theory, which is the prototype of a genuine sign problem for pure YM fields. For both these challenging problems we do not have final answers. We present the current status of our study.

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arXiv2021

Taylor expansions and Padé approximations for Lefschetz thimbles and beyond

Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model. Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex $μ_B$ plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration.

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arXiv2021

Lee-Yang edge singularities in 2+1 flavor QCD with imaginary chemical potential

We present results of the location of the closest singularities in the complex chemical potential plane using a novel method. These results are obtained with (2+1)-flavor of highly improved staggered quarks (HISQ) on lattices with temporal extent of Nt=4,6. We show that the scaling is consistent with the expected scaling of the Lee-Yang edge singularities in the vicinity of the Roberge-Weiss (RW) transition. We determine various non-universal parameters using 3D Ising model scaling functions that map QCD in the scaling region of the RW transition. Furthermore, as a preliminary result we discuss how the Lee-Yang edge singularity can be used to probe the chiral phase transition in QCD. The singularity obtained close to the chiral phase transition temperature Tc seems to be in agreement with the expected scaling of the Lee-Yang edge singularity. As an outlook, we discuss the scaling of the Lee-Yang edge singularity in the vicinity of a possible critical end point in QCD, at even lower temperatures. In the future, such a scaling analysis might hint on the existence and the location of the critical end point. The work presented here is a part of an ongoing project of Bielefeld Parma joint collaboration.

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arXiv2021

Lee-Yang edge singularities in lattice QCD : A systematic study of singularities in the complex $μ_B$ plane using rational approximations

A new approach is presented to explore the singularity structure of lattice QCD at imaginary chemical potential. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies in using rational (Padé) approximants for studying Lee Yang edge singularities. The motivation for using rational approximants will be exhibited. We will provide some confidence in our approach based on numerical experiments performed on well-motivated "toy models". Our focus lies in identifying singularities of the net-baryon number density in the complex $μ_B$ plane. To this end we have found signatures of the Roberge-Weiss critical point(and Chiral singularities -- subject to some caveats). In this contribution we will discuss the setup, simulation parameters and results obtained for 2+1 flavor QCD in the complex $μ_B/T$ plane.

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arXiv2021

Settling an old story: solution of the Thirring model in thimble regularization

Thimble regularisation of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many thimbles can contribute to the computation of the functional integrals. Semiclassical arguments would suggest that the fundamental thimble could be sufficient to get the correct answer, but this hypothesis has been proven not to hold true in general. A first example of this failure has been put forward in the context of the Thirring model: the dominant thimble approximation is valid only in given regions of the parameter space of the theory. Since then a complete solution of this (simple) model in thimble regularisation has been missing. In this paper we show that a full solution (taking the continuum limit) is indeed possible. It is possible thanks to a method we recently proposed which de facto evades the need to simulate on many thimbles.

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arXiv2020

Taylor expansions on Lefschetz thimbles (and not only that)

Thimble regularisation is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the fact that one in general needs to collect contributions coming from more than one thimble. Here we explore the idea of performing Taylor expansions on Lefschetz thimbles. We show that in some cases we can compute expansions in regions where only the dominant thimble contributes to the result in such a way that these (different, disjoint) regions can be bridged. This can most effectively be done via Padé approximants. In this way multi-thimble simulations can be circumvented. The approach can be trusted provided we can show that the analytic continuation we are performing is a legitimate one, which thing we can indeed show. We briefly discuss two prototypal computations, for which we obtained a very good control on the analytical structure (and singularities) of the results. All in all, the main strategy that we adopt is supposed to be valuable not only in the thimble approach, which thing we finally discuss.

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arXiv2020

One-thimble regularisation of lattice field theories: is it only a dream?

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble.

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arXiv2020

On the Lefschetz thimbles structure of the Thirring model

The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the integrals so that on each thimble the sign problem disappears. However, for systems in which more than one thimble contribute one is faced with the challenging task of collecting contributions coming from multiple thimbles. The Thirring model is a nice playground to test multi-thimble integration techniques; even in a low dimensional theory, the thimble structure can be rich. It has been shown since a few years that collecting the contribution of the dominant thimble is not enough to capture the full content of the theory. We report preliminary results on reconstructing the complete results from multiple thimble simulations.

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arXiv2018

Towards Lefschetz thimbles regularization of heavy-dense QCD

At finite density, lattice simulations are hindered by the well-known sign problem: for finite chemical potentials, the QCD action becomes complex and the Boltzmann weight $e^{-S}$ cannot be interpreted as a probability distribution to determine expectation values by Monte Carlo techniques. Different workarounds have been devised to study the QCD phase diagram, but their application is mostly limited to the region of small chemical potentials. The Lefschetz thimbles method takes a new approach in which one complexifies the theory and deforms the integration paths. By integrating over Lefschetz thimbles, the imaginary part of the action is kept constant and can be factored out, while $e^{-Re(S)}$ can be interpreted as a probability measure. The method has been applied in recent years to more or less difficult problems. Here we report preliminary results on Lefschetz thimbles regularization of heavy-dense QCD. While still simple, this is a very interesting problem. It is a first look at thimbles for QCD, although in a simplified, effective version. From an algorithmic point of view, it is a nice ground to test effectiveness of techniques we developed for multi thimbles simulations.

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arXiv2018

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order $O(β^{-7})$ in a ${\mathrm{SU}}(3)$ gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order $O(β^{-35})$ in a ${\mathrm{SU}}(3)$ gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.

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arXiv2018

Non perturbative physics from NSPT: renormalons, the gluon condensate and all that

Numerical Stochastic Perturbation Theory (NSPT) enables very high order computations in Lattice Gauge Theories. We report on the determination of the gluon condensate from lattice QCD measurements of the basic plaquette. This is a long standing problem, which was eventually solved a few years ago in pure gauge. In this context NSPT is crucial: it is actually the only tool enabling the subtraction of the power divergent contribution associated to the identity operator in the OPE for the plaquette. This subtraction is actually a delicate issue, since the perturbative expansion of the plaquette is on general ground expected to be an asymptotic one, due to renormalons. This in turn results in ambiguities and the separation of scales in the OPE does not correspond to a separation of perturbative and non-perturbative contributions. All in all, one needs to absorb the ambiguities attached to the perturbative series into the definition of the condensate itself, i.e. one needs a prescription. A possible one amounts to summing the perturbative series up to its minimal term, which means computing up to orders which only NSPT can aim at. Our computation is the first one in QCD, with massless staggered fermions. In order to remove the zero-mode of the gauge field, twisted boundary conditions are adopted for the latter, consistently coupled to fermions in the fundamental representation supplemented with smell degrees of freedom.

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arXiv2017

Simulating lattice field theories on multiple thimbles

Simulating thimble regularization of lattice field theory can be tricky when more than one thimble is to be taken into account. A couple of years ago we proposed a solution for this problem. More recently this solution proved to be effective in the case of 0+1 dimensional QCD. A few lessons we can learnt, including the role of symmetries and general hints on algorithmic solutions.

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arXiv2016

Simulating thimble regularization of lattice quantum field theories

Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow lines. The latter are the steepest ascent paths attached to critical points, i.e. the basic building blocks of thimbles. The measure to sample is thus dictated by the contribution of complete flow lines to the partition function. The algorithm is based on a heat bath sampling of the gaussian approximation of the thimble: this defines the proposals for a Metropolis-like accept/reject step. The effectiveness of the algorithm has been tested on a few models, e.g. the chiral random matrix model. We also discuss thimble regularization of gauge theories, and in particular the successfull application to 0+1 dimensional QCD and the status and prospects for Yang-Mills theories.

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arXiv2016

SculptStat: Statistical Analysis of Digital Sculpting Workflows

Targeted user studies are often employed to measure how well artists can perform specific tasks. But these studies cannot properly describe editing workflows as wholes, since they guide the artists both by choosing the tasks and by using simplified interfaces. In this paper, we investigate digital sculpting workflows used to produce detailed models. In our experiment design, artists can choose freely what and how to model. We recover whole-workflow trends with sophisticated statistical analyzes and validate these trends with goodness-of-fits measures. We record brush strokes and mesh snapshots by instrumenting a sculpting program and analyze the distribution of these properties and their spatial and temporal characteristics. We hired expert artists that can produce relatively sophisticated models in short time, since their workflows are representative of best practices. We analyze 13 meshes corresponding to roughly 25 thousand strokes in total. We found that artists work mainly with short strokes, with average stroke length dependent on model features rather than the artist itself. Temporally, artists do not work coarse-to-fine but rather in bursts. Spatially, artists focus on some selected regions by dedicating different amounts of edits and by applying different techniques. Spatio-temporally, artists return to work on the same area multiple times without any apparent periodicity. We release the entire dataset and all code used for the analyzes as reference for the community.

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arXiv2015

Thimble regularization at work: from toy models to chiral random matrix theories

We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex 0-dimensional phi^4 theory. Although very simple, this toy-model makes us appreciate a few key issues of the method. In particular, we will solve the model by a correct accounting of all the thimbles giving a contribution to the partition function and we will discuss a number of algorithmic solutions to simulate this (simple) model. We will then move to a chiral random matrix (CRM) theory. This is a somehow more realistic setting, giving us once again the chance to tackle the same couple of fundamental questions: how many thimbles contribute to the solution? how can we make sure that we correctly sample configurations on the thimble? Since the exact result is known for the observable we study (a condensate), we can verify that, in the region of parameters we studied, only one thimble contributes and that the algorithmic solution that we set up works well, despite its very crude nature. The deviation of results from phase quenched results highlights that in a certain region of parameter space there is a quite important sign problem. In view of this, the success of our thimble approach is quite a significant one.

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arXiv2015

High density QCD on a Lefschetz thimble?

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but - quite surprisingly - most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.

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arXiv2013

Monte Carlo simulations on the Lefschetz thimble: taming the sign problem

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to 8^4 using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that - at least in the case of the relativistic Bose gas - the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability - in principle - of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.

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