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

A study of QCD at finite density using complex Langevin dynamics.

Numerical simulations are a standard tool to investigate field theories innon-perturbative regimes. Typical algorithms used to evaluate path integralsin Euclidean space rely on importance sampling methods; i.e., aprobabilistic interpretation of the Boltzmann weight eS. However, manytheories of interest suffer from the infamous sign problem: the action iscomplex and the Boltzmann weight cannot be used as a probability distribution.Complex Langevin simulations allow numerical studies of theoriesthat exhibit the sign problem, such as QCD at finite density.In this thesis, we study methods to investigate the phase diagram of QCDin the temperature{chemical potential plane, using the complex Langevinmethod. We provide results on the phase diagram for the heavy-denseapproximation of QCD (HDQCD) for three spatial volumes, using complexLangevin and the gauge cooling technique. We also present polynomialfits of the critical temperature as function of the chemical potential foreach volume. Subsequently, we discuss instabilities encountered during thisstudy, which motivated a novel technique, named Dynamic Stabilisation,which will be introduced and the theoretical ideas behind it, explained.Dynamic stabilisation was, then, used in an investigation of the dependencyof the critical chemical potential on the hopping parameter. The two previousstudies were used to guide a second examination of the HDQCD phasediagram, focussed around the phase boundary.Lastly, we present preliminary results on the phase diagram of QCD withfully dynamical quarks at high temperatures. This shows that complexLangevin, augmented with gauge cooling and dynamic stabilisation, is suitedfor investigating QCD at finite chemical potential

Complex Langevin simulations and the QCD phase diagram: Recent developments

In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here we focus on the explicit computation of boundary terms, which provide an observable that can be used to check one of the criteria of correctness explicitly. We also present the method of Dynamic Stabilization and elaborate on recent results for fully dynamical QCD.Comment: 7 pages, 1 figure, 4 tables, to appear in EPJ

Harmonically trapped fermions in one dimension: A finite temperature lattice Monte Carlo study

We study a one-dimensional two-component Fermi gas in a harmonic trapping potential using finite temperature lattice quantum Monte Carlo methods. We are able to compute observables in the canonical ensemble via an efficient projective approach. Results for density profiles, correlations, as well as energy-related observables are presented for systems with up to 80 particles and various temperatures. Our simulations reproduce known numerical results and compare well against available experimental data close to the ground state, while at higher temperature they are benchmarked against the exact solution of the two particle system. This provides an indication that a standard lattice discretization is sufficient to capture the physics of the trapped system. In the special case of a spin-imbalanced gas, we find no sign problem in the parameter ranges studied, allowing access without the need of specialized methods. This includes simulations close to the ground state and at large population imbalance, where we present results for density correlations, indicating pairing at finite total momentum.Comment: 11 pages, 6 figure

Equation of state from complex Langevin simulations

We use complex Langevin simulations to study the QCD phase diagram with two light quark flavours. In this study, we use Wilson fermions with an intermediate pion mass of ∼ 480MeV. By studying thermodynamic quantities, in particular at lower temperatures, we are able to describe the equation of state