Philippe de Forcrand

Simulating QCD at finite density

In this review, I recall the nature and the inevitability of t he “sign problem” which plagues attempts to simulate lattice QCD at finite baryon density. I pre sent the main approaches used to circumvent the sign problem at small chemical potential. I sketch how one can predict analytically the severity of the sign problem, as well as the numerically accessible range of baryon densities. I review progress towards the determination of t he pseudo-critical temperature Tc(μ), and towards the identification of a possible QCD critical poi nt. Some promising advances with non-standard approaches are reviewed.

Relevance of center vortices to QCD

In a numerical experiment, we remove center vortices from an ensemble of lattice SU(2) gauge configurations. This removal adds short-range disorder. Nevertheless, we observe long-range order in the modified ensemble: confinement is lost and chiral symmetry is restored (together with trivial topology), proving that center vortices are responsible for both phenomena. As for the Abelian monopoles, they survive but their percolation properties are lost.

The chiral critical line of Nf = 2+1 QCD at zero and non-zero baryon density

We present numerical results for the location of the chiral critical line at finite temperature and zero and non-zero baryon density for QCD with Nf = 2 + 1 flavours of staggered fermions on lattices with temporal extent Nt = 4. For degenerate quark masses, we compare our results obtained with the exact RHMC algorithm with earlier, inexact R-algorithm results and find a reduction of 25% in the critical quark mass, for which the first order phase transition changes to a smooth crossover. Extending our analysis to non-degenerate quark masses, we map out the chiral critical line up to the neighbourhood of the physical point, which we confirm to be in the crossover region. Our data are consistent with a tricritical point at (mu,d = 0,ms ∼500) MeV. We also investigate the shift of the critical line with finite baryon density, by simulating with an imaginary chemical potential for which there is no sign problem. We observe this shift to be very small or, conversely, the critical endpoint µ c (mu,d,ms) to be extremely quark mass sensitive. Moreover, the sign of this shift is opposite to standard expectations. If confirmed on a finer lattice, it implies the absence of a critical endpoint for physical QCD at small chemical potential, or another revision of the QCD phase diagram. We critically examine earlier lattice determinations of the QCD critical point, and find them to be in no contradiction with our conclusion. Hence we argue that finer lattices are required to settle even the qualitative features of the QCD phase diagram.

Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD

We examine a new second-order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, 1/2, is about 10 times smaller than that of the standard second-order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al, and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in quantum Monte Carlo.

Topology of the SU (2) vacuum: a lattice study using improved cooling

We study the topological structure of the SU(2) vacuum at zero temperature: topological susceptibility, size, shape and distance distributions of the instantons. We use a cooling algorithm based on an improved action with scale invariant instanton solutions. This algorithm needs no monitoring or calibration, has an inherent cut off for dislocations and leaves unchanged instantons at physical scales. The physical relevance of our results is checked by studying the scaling and finite volume dependence. We obtain a susceptibility of (200(15) MeV)4. The instanton size distribution is peaked around 0.43 fm, and the distance distribution indicates a homogeneous, random spatial structure.

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence, from lattice simulations of QCD with three degenerate quark species, for two tricritical points in the (T, m) phase diagram at fixed imaginary chemical potential μ/T = iπ/3 mod2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary μ, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to nondegenerate and light quark masses is discussed.

Observing string breaking with Wilson loops

An uncontroversial observation of adjoint string breaking is proposed, while measuring the static potential from Wilson loops only. The overlap of the Wilson loop with the broken-string state is small, but non-vanishing, so that the broken-string groundstate can be seen if the Wilson loop is long enough. We demonstrate this in the context of the (2 + 1) dS U(2) adjoint static potential, using an improved

Systematic errors of Lüscher's fermion method and its extensions

Abstract We study the systematic errors of Luschers formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite β. We confirm the existence of an optimal window in the cutoff parameter ϵ, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.

The Gluon propagator without lattice Gribov copies

We study the gluon propagator in quenched lattice QCD using the Laplacian gauge which is free of lattice Gribov copies. We compare our results with those obtained in the Landau gauge on the lattice, as well as with various approximate solutions of the Dyson-Schwinger equations. We find a finite value;(445 MeV) 22 for the renormalized zero-momentum propagator ~taking our renormalization point at 1.943 GeV! and a pole mass ;6406140 MeV.

The static three-quark SU(3) and four-quark SU(4) potentials

We present results on the static three- and four-quark potentials in SU(3) and SU(4) respectively within quenched lattice QCD. We use an analytic multi-hit procedure for the time links and a variational approach to determine the ground state. The three- and four-quark potentials extracted are consistent with a sum of two-body potentials, possibly with a weak many-body component. The results give support to the