We study the nature of the finite temperature phase transition for three-flavor QCD. In particular we investigate the location of the critical endpoint along the three flavor symmetric line in the light quark mass region of the Columbia plot. In the study, the Iwasaki gauge action and the nonperturvatively O($a$) improved Wilson-Clover fermion action are employed. We newly generate data at $N_{\rm t}=12$ and set an upper bound of the critical pseudoscalar meson mass in the continuum limit $m_{\rm PS,E}\lesssim 110$MeV.
The finite temperature lattice QCD with N_f=2 nonperturbatively improved Wilson fermions is studied on 16^3 8 lattice. Using abelian projection after fixing to MA gauge we determine the transition temperature for m_π/m_ρ \sim 0.8.
We report the results of our quenched lattice simulations of the Wilson action with a nonperturbatively determined clover term at beta=6.2 and compare them with those of the standard Wilson action at the same beta value.
The critical temperature and the nature of the QCD finite temperature phase transition are determined for Nf=2 dynamical flavors of nonperturbatively improved Wilson fermions. The calculations are performed on large lattices with temporal extents Nt=12, 10 and 8, and lattice spacings down to a = 0.075 fm. We find the deconfinement and chiral phasetransitions to take place at the same temperature. Our results are in broad agreement with a second order phase transition in the chiral limit. The critical temperature at the physical quark mass is found to be Tc = 174(3)(6) MeV.
We investigate the finite temperature behavior of nonperturbatively improved clover fermions on lattices with temporal extent N_t=4 and 6. Unfortunately in the gauge coupling range, where the clover coefficient has been determined nonperturbatively, the finite temperature crossover/transition occurs at heavy pseudoscalar masses and large pseudoscalar to vector meson mass ratios. However, on an N_t=6 lattice the thermal crossover for the improved fermions is much smoother than for unimproved Wilson fermions and no strange metastable behavior is observed.
We present a preliminary calculation of the charmed meson spectrum using the 2+1 flavor domain wall fermion lattice configurations currently being generated by the RBC and UKQCD collaborations. The calculation is performed using the 3-parameter, relativistic heavy quark action with nonperturbatively determined coefficients. We will also demonstrate a step-scaling procedure for determining these coefficients nonperturbatively using a series of quenched, gauge field ensembles generated for three different lattice spacings.
We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-$N_t$ approach, it is easy to keep scaling violations small at low temperature in the fixed scale approach. We study 2+1 flavor QCD at light quark mass co…
We give an update on our current project to determine the transition temperature and the order of the deconfinement transition in the chiral limit of two flavour QCD. We use nonperturbatively O(a) improved Wilson fermions of the Sheikholeslami-Wohlert type, employing the efficient deflation accelerated DDHMC algorithm. We start at lattices with N_t>=12 and pion masses below 600 MeV, aiming at chiral and continuum limits with light quarks.
A lot of effort in lattice simulations over the last years has been devoted to studies of the QCD deconfinement transition. Most state-of-the-art simulations use rooted staggered fermions, while Wilson fermions are affected by large systematic uncertainties, such as coarse lattices or heavy sea quarks. Here we report on an ongoing study of the transition, using two degenerate flavours of nonperturbatively $\Ord(a)$ improved Wilson fermions. We start with $N_{t}=12$ and 16 lattices and pion masses of 600 to 450 MeV, aiming at chiral and continuum limits with light quarks.
The critical temperature is computed for N_f = 2 dynamical flavors of nonperturbatively improved Wilson fermions. The new simulations are performed on lattices 40^3 x 14 with lattice spacing and pion mass about 0.08 fm and 200 MeV, respectively. We find the deconfinement and chiral phase transitions to coincide within numerical precision. Our results are in broad agreement with a second order phase transition in the chiral limit. The critical temperature at the physical quark mass is found to be T_c = 172(3)(6) MeV.
We present preliminary results of the PACS-CS project which simulates 2+1 flavor lattice QCD toward the physical point with the nonperturbatively O(a)-improved Wilson quark action and the Iwasaki gauge action. Calculations are carried out at beta=1.9 on a 32^3x64 lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. The resulting pseudoscalar meson masses range from 730 MeV down to 210 MeV. We discuss the physical results including the chiral analysis in the pseudoscalar meson sector and the hadron spectrum. Some algorithmic issues are also discussed.
We study the (2+1)-flavor QCD at nonzero temperatures using nonperturbatively improved Wilson quarks of the physical masses by the fixed scale approach. We perform physical point simulations at finite temperatures with the coupling parameters which were adopted by the PACS-CS Collaboration in their studies using the reweighting technique. Zero temperature values are obtained on the PACS-CS configurations which are open to the public on the ILDG/JLDG. Finite temperature configurations are generated with the RHMC algorithm. The lattice sizes are $32^3 \times N_t$ with $N_t=14$, 13, $\cdots$, 4 w…
We compute the nonperturbative quark mass RG-running in the range $Λ_{QCD}\lessapproxμ\lessapprox M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schrödinger functional (SF) boundary conditions, employing the configurations of 1802.05243, while valence quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with chirally rotated Schrödinger functional boundary conditions ($χ$SF). Our result is compatible with its SF counterpart of ref.1802.05243, confirming the universalit…
We present preliminary results for the topological charge and susceptibility determined from the low-lying eigenmodes of the Wilson-Dirac operator. These modes have been computed on dynamical configurations with Nf=2 non-perturbatively improved Wilson fermions. We compare our results with the eigenmodes of fermions in the quenched approximation.
We present preliminary results for the light harden spectrum in $N_f=2+1$ lattice QCD obtained with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Simulations are carried out at $β=1.90$ on a $32^3 \times 64$ lattice using the PACS-CS computer. We employ Lüscher's domain-decomposed HMC algorithm to reduce the up-down quark masses toward the physical value. The pseudoscalar meson masses range from 730 MeV down to 210 MeV. We compare the light harden spectrum extrapolated to the physical point with the experimental values.
We explore sea quark effects in the light hadron mass spectrum in a simulation of two-flavor QCD using the nonperturbatively O(a)-improved Wilson fermion action. In order to identify finite-size effects, light meson masses are measured on 12^3x48, 16^3x48 and 20^3x48 lattices with a~0.1 fm. On the largest lattice, where the finite-size effect is negligible, we find a significant increase of the strange vector meson mass compared to the quenched approximation. We also investigate the quark mass dependence of pseudoscalar meson masses and decay constants and test the consistency with (partially …
We demonstrate that in the topologically trivial gauge sector the Ginsparg-Wilson relation for lattice Dirac operators admits an exactly gauge invariant path integral formulation of the Weyl fermions on a lattice.
Stabilized Wilson fermions are a reformulation of Wilson clover fermions that incorporates several numerical stabilizing techniques, but also a local change of the fermion action - the original clover term being replaced with an exponentiated version of it. We intend to apply the stabilized Wilson fermions toolbox to the thermodynamics of QCD, starting on the $N_f=3$ symmetric line on the Columbia plot, and to compare the results with those obtained with other fermion discretizations.
The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.
We show that it is possible to construct a lattice Schroedinger functional for standard Wilson fermions, where the expectation values of ${\cal R}_5$-even operators are O($a$) improved, up to terms coming from the boundaries.
In the simulation of QCD with 2+1 flavors of Wilson fermions, the positivity of the fermion determinant is generally assumed. We present evidence that this assumption is in general not justified and discuss the consequences of this finding.
We show rigorously that for general Ginsparg-Wilson fermions the dimensions of the geometric eigenspace and of the algebraic one for zero modes agree so that the index theorem on the lattice is not spoiled by unwanted additional terms.
I report on cost estimates and algorithmic performance in simulations using 2 flavours of non-perturbatively O(a) improved Wilson quarks together with the Wilson plaquette action.
We study strong-coupling lattice QCD with staggered-Wilson fermions, with emphasis on discrete symmetries and possibility of their spontaneous breaking. We perform hopping parameter expansion and effective potential analyses in the strong-coupling limit. From gap equations we find nonzero pion condensate in some range of a mass parameter, which indicates existence of the parity-broken phase in lattice QCD with staggered-Wilson fermions. We also find massless pions and PCAC relations around second-order phase boundary. These results suggest that we can take a chiral limit by tuning a mass param…
We discuss the improvement of bilinear fermionic operators for Ginsparg-Wilson fermions. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.
It was shown recently by I. Horvath that lattice fermions obeying the standard form of the Ginsparg-Wilson relation cannot be ultralocal. However, there are more general forms of the Ginsparg-Wilson relation, which also guarantee the physical properties related to chirality, but which are not covered by Horvath's consideration. Here we present a proof which applies to all Ginsparg-Wilson fermions, demonstrating that they can only be local in the sense of an exponential decay of their couplings, but not ultralocal.
We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.
In this proceeding contribution we report on the ongoing effort to understand and simulate Wilson twisted mass fermions in the so called epsilon regime.
We test an algebraic algorithm based on the coordinate-space method, evaluating with high accuracy the critical mass for Wilson fermions in lattice QCD at two loops. We test the results by using different types of infrared regularization.
We study the two-dimensional lattice Gross--Neveu model with Wilson twisted mass fermions in order to explore the phase structure in this setup. In particular, we investigate the behaviour of the phase transitions found earlier with standard Wilson fermions as a function of the twisted mass parameter $μ$. We find that qualitatively the dependence of the phase transitions on $μ$ is very similar to the case of lattice QCD.
We analytically investigate the 2-dimensional Gross-Neveu model at finite temperature and density using Wilson fermion action. The relation between the phase structure on the lattice and that in the continuum is clarified.
Using Schroedinger functional techniques, we determine the coefficient of the clover term necessary for non-perturbative O(a) improvement of hypercubic smeared Wilson fermions on a quenched plaquette action background. Unlike for unsmeared Wilson fermions, the resulting clover coefficients are close to the tree-level value even at coarse lattice spacings, indicating the absence of large cutoff effects. A number of exploratory tests are also performed with the improved action.
We present a new staggered discretization of the Dirac operator. In comparison with standard staggered fermions, real and imaginary parts are located in different nodes. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. Contrary to usual staggered fermions, we have no exact chiral symmetry but obtain a generalization of the Ginsparg-Wilson relation.
We present recent results for meson screening masses with quenched Wilson fermions above and below the confinement- deconfinement phase transition. The action used in the simulation is the Sheikholeslami Wohlert action. The quark masses are chosen to be in a range going from light quarks up to the mass of the charm quark. These results are compared with zero temperature Wilson and high temperature staggered data.
For QCD with Wilson fermions at isospin chemical potential we study the finite phase transition on an $8^3\times4$ lattice at $κ=0.15$. We use two gauge actions: Wilson action and DBW2 action. Both actions give the same results. The phase diagram is qualitatively similar to the one obtained for QCD at small baryon chemical potential. We also calculate the number density for various isospin chemical potentials.
Vectorial and anomaly free chiral U(1) fermion models on a 2d finite lattice are considered. It is demonstrated both numerically and analytically that introduction of Pauli -- Villars type regularization supresses the symmetry breaking effects caused by the Wilson term.
The flavour singlet axial Ward identity with Osterwalder-Seiler twisted mass Wilson fermion action is studied on a finite lattice, with finite fermion mass and the Wilson parameter r up to 1. Approach to the infinite volume chiral limit and emergence of the anomaly is significantly better than that obtained with O(a) and O(a^2) improved fermion actions. We have shown explicitly that up to O(g^2), parity violating terms cancel in the Ward identity even at finite volume and finite lattice spacing.
We compute the O(g^2) contribution to the thermodynamic pressure for Wilson fermions in the standard, the twisted mass, and clover improved formulation in lattice perturbation theory, including finite mass effects. We compare the continuum approaches of these discretizations for the massive ideal and interacting gas. In all cases, for N_t \geq 8 cutoff effects of Wilson type fermions are comparable to those of staggered fermions, but asymptotic scaling requires $N_τ>10$.
We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on t…
A comprehensive number of integrals emerging in one-loop computations in a gauge perturbation theory on the lattice with Wilson fermions at $r=1$ is computed using the Burgio--Caracciolo--Pelissetto algorithm and the FORM package. An explicit analytical form of the recursion relations needed for such computations is presented.
We apply the coordinate-space method by Luescher and Weisz to the computation of two-loop diagrams in full QCD with Wilson fermions on the lattice. The essential ingredient is the high-precision determination of mixed fermionic-bosonic propagators.
A preconditioning for the Wilson fermion matrix on the lattice is defined which is particularly suited to the case when the temporal lattice spacing is much smaller than the spatial one. Details on the implementation of the scheme are given. The method is tested in numerical studies of QCD on anisotropic lattices.
We present results from simulations of two dynamical flavors of improved Wilson fermions with nHYP smeared gauge links. We demonstrate that the simulation is stable at a pseudo-scalar mass of 360MeV, a 2.1fm box and a lattice spacing of 0.13fm.
In this proceeding contribution we report on the ongoing effort to simulate Wilson-type fermions in the so called epsilon regime of chiral perturbation theory. We present results for the chiral condensate and the pseudoscalar decay constant obtained with Wilson twisted mass fermions employing two lattice spacings, two different physical volumes and several quark masses. With this set of simulations we make a first attempt to estimate the systematic uncertainties.
We discuss a number of lattice fermion actions solving the Ginsparg-Wilson relation. We also consider short ranged approximate solutions. In particular, we are interested in reducing the lattice artifacts, while avoiding (or suppressing) additive mass renormalization. In this context, we also arrive at a formulation of improved domain wall fermions.
Lattice fermions obeying the Ginsparg-Wilson relation do correctly represent the physical properties related to chirality. This can be achieved by local fermions, which involve an infinite number of couplings, however. For practical purposes, it is useful to first construct approximate Ginsparg-Wilson fermions within a short range. We report on a successful construction in QCD at β=6. The good quality of the approximation is observed from the spectrum, which is situated close to a Ginsparg-Wilson circle. These fermions also provide an excellent approximation to rotational symmetry and they are…
We study strong-coupling lattice QCD with staggered-Wilson fermions, with an emphasis on the possibility of spontaneous parity breaking. We perform effective potential analysis in the strong-coupling limit. From gap equations we find the pion condensate becomes nonzero in some range of a mass parameter, which indicates the existence of the parity-broken phase. We also find massless pions and PCAC relations around the second-order phase boundary. These results suggest that we can take the chiral limit by tuning a mass parameter in lattice QCD with staggered-Wilson fermions as with the Wilson fe…
We present a simulation algorithm for Wilson fermions based on the exact hopping expansion of the fermion action. The algorithm essentially eliminates critical slowing down by sampling the fermionic two-point correlation function and it allows simulations directly in the massless limit. As illustrative examples, the algorithm is applied to the Gross-Neveu and the Schwinger model, the latter in the strong coupling limit.
Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice. For free fermion system exact chiral symmetry can be implemented without species doubling. In the presence of gauge couplings the chiral symmetry is violated. We show that the divergence of the axial vector current is related to the chiral anomaly in the classical continuum limit.
