arXiv subjects

Philippe de Forcrand

Publications and source records attributed to Philippe de Forcrand.

At least 19 recordsLinked to original sources

arXiv2022

Diquark properties from full QCD lattice simulations

We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical $m_π$. We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have "good" scalar, $\bar{3}_F$, $\bar{3}_c$, $J^P=0^+$, and "bad" axial vector, $6_F$, $\bar{3}_c$, $J^P=1^+$, quantum numbers, and a bad-good mass difference for $ud$ flavors, $198(4)~\rm{MeV}$, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the "good" diquark channel. We extract a corresponding diquark size of $\sim 0.6~\rm{fm}$ and perform a first exploration of the "good" diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

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arXiv2018

Topological Susceptibility of the 2d O(3) Model under Gradient Flow

The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility $χ_{\rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $χ_{\rm t}\, ξ^{2}$ diverges at large correlation length $ξ$. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces $χ_{\rm t}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $ξ/2$, we do still not observe evidence of continuum scaling.

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arXiv2018

Taylor expansion and the Cauchy Residue Theorem for finite-density QCD

We present an update on our efforts to determine the Taylor coefficients of the $μ/T$ expansion of the pressure for finite-density QCD. Here, we explore alternatives based on the Cauchy Residue Theorem, which allows us to use a discretized contour to determine the desired spectral moments occurring in the Taylor expansion of QCD at zero chemical potential.

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arXiv2018

RHMC with Block Solvers and Multiple Pseudofermions

The dominant cost of most lattice QCD simulations is the inversion of the Dirac operator required to calculate the force term in the RHMC update. One way to improve this situation is to use multiple pseudofermions, which reduces the size and variance of this force and hence allows a larger integration step size to be used. This means fewer force term calculations are required, but at the cost of having to invert the Dirac operator for each pseudofermion field. This bottleneck can be addressed: recently there has been renewed interest in the use of block Krylov solvers, which can solve multiple right hand side vectors with significantly fewer iterations than are required if each vector is solved using a separate Krylov solver. We combine these two ideas, achieving a significant speed-up of RHMC lattice QCD simulations.

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arXiv2018

Strong-Coupling Lattice QCD on Anisotropic Lattices

Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalisation of the anisotropy coupling in strongly-coupled SU($N$) or U($N$) lattice QCD with massless staggered fermions. We then compute the renormalised anisotropy, and the strong-coupling analogue of Karsch's coefficients (the running anisotropy), for $N=3$. We achieve high precision by combining diagrammatic Monte Carlo and multi-histogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass, and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong coupling limit at zero temperature.

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arXiv2017

Topological Susceptibility under Gradient Flow

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $χ_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $χ_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $ξ^{2}$). This ongoing study is based on direct measurements of $χ_{\rm t}$ in $L \times L$ lattices, at $L/ξ\simeq 6$.

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arXiv2017

Spin models in complex magnetic fields: a hard sign problem

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.

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arXiv2017

Alternatives to the stochastic "noise vector" approach

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with "noise vectors" sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator.

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arXiv2017

Topology in the 2d Heisenberg Model under Gradient Flow

The 2d Heisenberg model --- or 2d O(3) model --- is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge $Q$ can still be defined such that $Q \in \mathbb{Z}$. It has generally been observed, however, that the topological susceptibility $χ_{\rm t} = \langle Q^2 \rangle / V$ does not scale properly in the continuum limit, i.e. that the quantity $χ_{\rm t} ξ^2$ diverges for $ξ\to \infty$ (where $ξ$ is the correlation length in lattice units). Here we address the question whether or not this divergence persists after the application of the Gradient Flow.

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arXiv2017

A Worm Algorithm for the Lattice CP(N-1) Model

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arXiv2017

Worm Algorithm for CP(N-1) Model

The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D CP(N-1) on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice CP(N-1) model has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular CP(N-1) lattice actions and exhibit marked differences in their approach to the continuum limit.

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arXiv2017

Continuum limit and universality of the Columbia plot

Results on the thermal transition of QCD with 3 degenerate flavors, in the lower-left corner of the Columbia plot, are puzzling. The transition is expected to be first-order for massless quarks, and to remain so for a range of quark masses until it turns second-order at a critical quark mass. But this critical quark mass and resulting "pion" mass disagree violently between Wilson and staggered fermions at finite lattice spacing, and decrease sharply with the lattice spacing, for staggered fermions at least. To clarify this puzzle and eliminate potential systematic effects from rooting, we study the 4-flavor theory with staggered fermions, on lattices with 4 to 10 time-slices. Our results are qualitatively similar to the 3-flavor case, so that rooting is not an issue. However, dramatic cutoff effects are visible, even on our finest lattices. Universality implies that cutoff effects for Wilson fermions are even more dramatic. In order to obtain a first-order thermal transition in the continuum theory, extremely light quarks are needed.

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arXiv2017

Thermodynamics of strongly-coupled lattice QCD in the chiral limit

In the strong coupling limit, $n$-point functions in lattice QCD with staggered fermions can be rewritten exactly as sums over constrained configurations of monomers, dimers, and baryon loops covering the spacetime lattice. Worm algorithms provide efficient global sampling methods over such ensembles, and are particularly efficient in the chiral limit. We study the thermodynamics of strongly-coupled U(3) and SU(3) lattice QCD with one massless staggered fermion using such methods, and compare the results with the relativistic pion gas down to low temperatures O(15 MeV).

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arXiv2016

Oscillating propagators in heavy-dense QCD

Using Monte Carlo simulations and extended mean field theory calculations we show that the $3$-dimensional $Z_3$ spin model with complex external fields has non-monotonic spatial correlators in some regions of its parameter space. This model serves as a proxy for heavy-dense QCD in $(3+1)$ dimensions. Non-monotonic spatial correlators are intrinsically related to a complex mass spectrum and a liquid-like (or crystalline) behavior. A liquid phase could have implications for heavy-ion experiments, where it could leave detectable signals in the spatial correlations of baryons.

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arXiv2016

The Slab Method to Measure the Topological Susceptibility

In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to measure the topological susceptibility chi_t. We test a method to measure chi_t even if configurations from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as "slab". This enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models and for 2-flavour QCD. In the latter case, the gradient flow is applied for the smoothing of the gauge configurations, and the slab method results for chi_t are stable over a broad range of flow times.

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arXiv2016

Sampling of General Correlators in Worm Algorithm-based Simulations

Using the complex $ϕ^4$-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator $<ϕ^{*}(x)ϕ(y)>$, but also more general correlators such as $<|ϕ(x)||ϕ(y)|>$ or $<\text{arg}(ϕ(x))\text{arg}(ϕ(y))>$, as well as condensates like $<|ϕ|>$, can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models.

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arXiv2016

Aspects of topological actions on the lattice

We consider a lattice action which forbids large fields, and which remains invariant under smooth deformations of the field. Such a "topological" action depends on one parameter, the field cutoff, but does not have a classical continuum limit as this cutoff approaches zero. We study the properties of such an action in 4d compact U(1) lattice gauge theory, and compare them with those of the Wilson action. In both cases, we find a weakly first-order transition separating a confining phase where monopoles condense, and a Coulomb phase where monopoles are exponentially suppressed. We also find a different, critical value of the field cutoff where monopoles completely disappear. Finally, we show that a topological action simplifies the measurement of the free energy.

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arXiv2016

Two-Flavor Lattice QCD with a Finite Density of Heavy Quarks: Heavy-Dense Limit and "Particle-Hole" Symmetry

We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate ($μ$,T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling $β$. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.

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