Dynamical stabilisation of complex Langevin simulations of QCD

The ability to describe strongly interacting matter at finite temperature and baryon density provides the means to determine, for instance, the equation of state of QCD at non-zero baryon chemical potential. From a theoretical point of view, direct lattice simulations are hindered by the numerical sign problem, which prevents the use of traditional methods based on importance sampling. Despite recent successes, simulations using the complex Langevin method have been shown to exhibit instabilities, which cause convergence to wrong results. We introduce and discuss the method of Dynamic Stabilisation (DS), a modification of the complex Langevin process aimed at solving these instabilities. We present results of DS being applied to the heavy-dense approximation of QCD, as well as QCD with staggered fermions at zero chemical potential and finite chemical potential at high temperature. Our findings show that DS can successfully deal with the aforementioned instabilities, opening the way for further progress.Comment: 11 pages, 15 figures and 2 tables; Added acknowledgment

Improved convergence of Complex Langevin simulations

The sign problem appears in lattice QCD as soon as a non-zero chemical potential is introduced. This prevents direct simulations to determine the phase structure of the strongly interacting matter. Complex Langevin methods have been successfully used for various models or approximations of QCD. However, in some scenarios it converges to incorrect results. We present developments of our new method that helps to improve the convergence by keeping the system closer to the SU(3) manifold and discuss preliminary tests and results.Comment: 7 pages, 6 figures, talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), Granada, Spai

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 $\mu/T$ 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.Comment: 6 pages, 4 figures, talk presented at the 36th Annual International Symposium on Lattice Field Theory, July 22-28, 2018, East Lansing, MI, US

Lattice calculations of the leading hadronic contribution to (g-2)_mu

We report on our ongoing project to calculate the leading hadronic contribution to the anomalous magnetic moment of the muon a_mu^HLO using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. In this study, we changed the vacuum polarisation tensor to a combination of local and point-split currents which significantly reduces the numerical effort. Partially twisted boundary conditions allow us to improve the momentum resolution of the vacuum polarisation tensor and therefore the determination of the leading hadronic contribution to (g-2)_mu. We also extended the range of ensembles to include a pion mass below 200 MeV which allows us to check the non-trivial chiral behaviour of a_mu^HLO.Comment: 7 pages, 3 figures, 1 table, talk presented at the 30th International Symposium on Lattice Field Theory (Lattice2012), Cairns, Australi

Improved interpolating fields for hadrons at non-vanishing momentum

We demonstrate that a reduction in the noise-to-signal ratio may be obtained for hadrons at non-zero momenta whilst maintaining a good overlap with the ground state through a generalisation of Gaussian/Wuppertal smearing. The use of an anisotropic smearing wavefunction is motivated by the physical picture of a boosted hadron.Comment: 7 pages, 6 figures, poster presented at the 30th International Symposium on Lattice Field Theory (Lattice 2012), Cairns, Australia, June 24-29, 201

The Shape of Covariantly Smeared Sources in Lattice QCD

Covariantly smeared sources are commonly used in lattice QCD to enhance the projection onto the ground state. Here we investigate the dependence of their shape on the gauge field background and find that the presence of localized concentrations of magnetic field can lead to strong distortions which reduce the smearing radii achievable by iterative smearing prescriptions. In particular, as $a\to 0$, iterative procedures like Jacobi smearing require increasingly large iteration counts in order to reach physically-sized smearing radii $r_{sm}\sim$ 0.5 fm, and the resulting sources are strongly distorted. To bypass this issue, we propose a covariant smearing procedure (``free-form smearing'') that allows us to create arbitrarily shaped sources, including in particular Gaussians of arbitrary radius.Comment: 1+15 pages, 7 figures (24 pdf images