The spectral projectors method is a way to obtain a theoretically well posed definition of the topological susceptibility on the lattice. Up to now this method has been defined and applied only to Wilson fermions. The goal of this work is to extend the method to staggered fermions, giving a definition for the staggered topological susceptibility and testing it in the pure $SU(3)$ gauge theory. Besides, we also generalize the method to higher-order cumulants of the topological charge distribution.
We extend the spectral projectors method to staggered fermions. Applying the index theorem to the staggered Dirac operator it is possible to work out an expression for the topological susceptibility which depends only on the orthogonal projectors on quasi zero-modes, as it has already been done for Dirac-Wilson fermions. Besides, we generalize this method deriving analogous expressions for all higher-order coefficients in the $θ$-expansion of the vacuum energy.
We present preliminary lattice results for the topological susceptibility in high-$T$ $N_f=2+1$ QCD obtained discretizing this observable via spectral projectors on eigenmodes of the staggered operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the continuum scaling of the gluonic susceptibility at high $T$, related to the choice of non-chiral fermions in the action.
The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we focus on the topological susceptibility, related to the axion mass. We present lattice results for the topological susceptibility in QCD at high temperatures obtained by discretizing this observable via spectral projectors on eigenmodes of the staggered Dirac operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral…
We compute the topological susceptibility of $N_f=2+1$ QCD with physical quark masses in the high-temperature phase, using numerical simulations of the theory discretized on a space-time lattice. More precisely we estimate the topological susceptibility for five temperatures in the range from $\sim200$ MeV up to $\sim600$ MeV, adopting the spectral projectors definition of the topological charge based on the staggered Dirac operator. This strategy turns out to be effective in reducing the large lattice artifacts which affect the standard gluonic definition, making it possible to perform a reli…
It is conventional wisdom that staggered fermions do not feel gauge field topology. However, the response of staggered fermion eigenmodes to the topology of the gauge field can depend quite sensitively on the way in which the staggered fermion action is improved. We study this issue using a variety of improved staggered quark actions. We observe that the separation between the ``would be'' zero modes and the non-chiral modes increases with the level of improvement. This enables the ``zero modes'' to be identified unambiguously. The distribution of the remaining non-chiral modes is compared wit…
We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero. The smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are thus insensitive to gauge field topology. On the smeared configurations, $4ν$ eigenvalues go to zero in agreement with the index theorem.
We compare the lower edge spectral fluctuations of the staggered lattice Dirac operator for the Schwinger model with the predictions of chiral Random Matrix Theory (chRMT). We verify their range of applicability, checking in particular the role of non-trivial topological sectors and the flavor symmetry of the staggered fermions for finite lattice spacing. Approaching the continuum limit we indeed find clear signals for topological modes in the eigenvalue spectrum. These findings indicate problems in the verification of the chRMT predictions.
Based on a large number of smearing steps, we classify SU(3) gauge field configurations in different topological sectors. For each sector we compare the exact analytical predictions for the microscopic Dirac operator spectrum of quenched staggered fermions. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero, showing explicitly that the smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are insensitive to gauge field topology. On the smeared configurations, $4ν$ eigenvalues clearly separate out …
The spectral properties of a variety of improved staggered operators are studied in quenched QCD. The systematic dependence of the infrared eigenvalue spectrum on i) improvement in the staggered operator, ii) improvement in the gauge field action, iii) lattice spacing and iv) lattice volume, is analyzed. It is observed that eigenmodes with small eigenvalues and large chirality appear as the level of improvement increases or as one approaches the continuum limit. These eigenmodes can be identified as the ``zero modes'' which contribute to the chirality associated, via the index theorem, with th…
We discuss the construction of a chiral random matrix model for staggered fermions. This model includes $O(a^2)$ corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing ($a$) of the Dirac matrix produces the term which gives the dominant contribution to the observed taste splitting in the pion masses. A more careful analysis can include extra terms which are also consistent with the symmetries of staggered fermions. Lastly I wil…
We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a Symanzik-improved gluon action. For the improved Dirac operators we find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as predicted by the continuum Index Theorem, and the expectation values of their chirality are large for the most improved actions (approx 0.7). T…
We report the results of a numerical study of staggered overlap fermions, following the construction of Adams which reduces the number of tastes from 4 to 2 without fine-tuning. We study the sensitivity of the operator to the topology of the gauge field, its locality and its robustness to fluctuations of the gauge field. We make a first estimate of the computing cost of a quark propagator calculation, and compare with Neuberger's overlap.
The rooting procedure commonly used with staggered fermions does not correctly treat non-perturbative effects associated with gauge field topology. In practice these effects are small for the physics of flavor non-singlet particles. However large uncontrolled systematic errors are expected for flavor singlet issues, such as the mass of the eta prime meson. While the relative speed of the algorithm in large scale simulations may justify its use, the method is an approximation and should not be promoted as a first principles approach to the strong interactions.
The behavior of staggered domain wall fermions in the presence of gauge fields is presented. In particular, their response to gauge fields with nontrivial topology is discussed.
We study the topological properties of full QCD with four flavours of dynamical staggered fermions. In particular the topological susceptibility is measured and the problem of the determination of its first derivative is discussed.
We study the finite temperature transition in QCD with two flavors of dynamical fermions at a pseudoscalar pion mass of about 350 MeV. We use lattices with temporal extent of $N_t$=8, 10 and 12. For the first time in the literature a continuum limit is carried out for several observables with dynamical overlap fermions. These findings are compared with results obtained within the staggered fermion formalism at the same pion masses and extrapolated to the continuum limit. The presented results correspond to fixed topology and its effect is studied in the staggered case. Nice agreement is found …
We use the two-dimensional Schwinger model to investigate how lattice fermions perceive the global topological charge $q\in\mathbf{Z}$ of a given gauge background $U$. After a warm-up part devoted to staggered, Adams, Wilson and naive fermions, we consider Karsten-Wilczek and Borici-Creutz fermions, which are in the class of minimally doubled lattice fermion actions. We focus on the eigenvalue spectrum and the chiralities of the pertinent eigenmodes. Without modification both minimally doubled actions are found to be insensitive to topology, but in either case it is possible to define a suitab…
A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field topology in accordance with the Index Theorem. The key idea is to consider the spectral flow of a certain hermitian version of the staggered Dirac operator. The staggered fermion index thus obtained can be used as a new way to assign the topological charge of lattice gauge fields. In a numerical study in U(1) backgrounds in 2 dimensions it is found to perform as we…
The introduction of non-orthogonal electric and magnetic fields in the QCD vacuum enhances the weight of topological sectors with a nonzero topological charge. For weak fields, there is a linear response for the expectation value of the topological charge. We study this linear response and relate it to the QCD correction to the axion-photon coupling. We also analyse the magnetic field dependence of the topological susceptibility for a range of temperatures around $T_c$. In this work we use lattice simulations with improved staggered quarks at physical masses, including background magnetic and …
We study topological properties of SU(3) gauge theory using improved cooling. In the absence of fermions, we measure a topological susceptibility of $(182(8) MeV)^4$ and an instanton size $\sim 0.6$ fm. In the presence of light staggered fermions and across the chiral transition, the susceptibility drops in a manner consistent with the quenched case, and the instanton size changes little. No significant formation of bound instanton-antiinstanton pairs is observed, in particular not along the Euclidean time direction for $T > T_c$.
In this paper we study the properties of QCD at nonzero chiral density $ρ_5$, which is introduced through chiral chemical potential $μ_5$. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that $ρ_5$ is generated at nonzero $μ_5$ and in the chiral limit observe $ρ_5 \sim Λ_{QCD}^2 μ_5$. We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility $χ_{\mbox{\footnotesize top}}$ and string tension $σ$ for various values of $μ_5$. We observed that both s…
We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming…
In this paper, we show a comparison of different definitions of the topological charge on the lattice. We concentrate on one small-volume ensemble with 2 flavours of dynamical, maximally twisted mass fermions and use three more ensembles to analyze the approach to the continuum limit. We investigate several fermionic and gluonic definitions. The former include the index of the overlap Dirac operator, the spectral flow of the Wilson--Dirac operator and the spectral projectors. For the latter, we take into account different discretizations of the topological charge operator and various smoothing…
