Nature of the QCD Transition with Chiral Fermions

Principal Investigator:
Kálmán Szabó

Forschungszentrum Jülich GmbH (Germany)

Local Project ID:

HPC Platform used:

Date published:

One of the important properties of Quantum Chromodynamics is that the transition that separates the phase of protons, neutrons and other hadrons at low temperatures from a phase of quarks and gluons at high temperature is smooth, as opposed to an ordinary phase transition that is observed for example when water vaporizes. Physicists call it a crossover transition.

The crossover nature of the transition gives a strong background for heavy ion physics, both for phenomenology and for the experiments. Furthermore, it is one of the most important parts of our knowledge concerning the early Universe, where this transition actually took place shortly after the Big Bang. This is the reason why we do not detect large fragments of strange quarks (strangelets) like we have different nuclei with up and down quarks all around. If an ordinary phase transition took place in the early Universe with bubbles which grow and collide, objects like strangelets would be inevitable.

The nature of the transition was established more than ten years ago in the paper [1] using a technique, called Lattice Quantum Chromodynamics. The computations were done on the state-of-the-art supercomputer of the time, on the pre-predecessor of HPC system JUQUEEN at JSC. Since then the result reached more than 1000 citations, which is the highest value of the last 20 years of lattice investigations. The result of Reference [1] has stood the test of time, even if the lattice sizes were very small by today’s standards. Because of the spotlight this result enjoys, it is highly desirable to improve the computations of [1].

Using the computer resources of JUQUEEN we revisited the nature of the QCD transition and set out to improve the procedure of Reference [1] by several means. First, we use an improved lattice discretization, that has much smaller lattice artefacts than the one in [1]. Second, we made simulations at around 10 different temperature values, so we can map the chiral susceptibility peak with a much finer resolution than before. As a third improvement, we use lattice spacings Nt = 8, 10, 12, 16 as opposed to Nt= 6, 8, 10 of Reference [1]. (Larger Nt means better discretization.) Our best lattice spacing is about a factor 3xcloser to the continuum limit than the best one in [1]. Also we generated much more statistics than before, so we can now clearly see the volume dependence of the result. Our earlier findings were consistent with no volume dependence over a large range of volumes.

We use a technique called finite volume scaling to establish the nature of the transition. In this approach one investigates the behaviour of an appropriate observable as a function of the volume: if a singularity appears as the volume is increased, then we have a real phase transition, otherwise a crossover. We chose the so-called renormalized chiral susceptibilty as our test observable. Figure 1 shows its peak in the transition region for four different lattice volumes and for a lattice spacing of Nt= 8.

After performing the continuum extrapolations our preliminary conclusion is the following: the height of the chiral susceptibility peak decreases with increasing volume, which very strongly disfavors any singularity in the infinite volume limit and therefore the real phase transition scenario. The result of Reference [1] seems to be confirmed by this improved investigation.

[1] Y. Aoki et al. The Order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature 443 (2006)

Scientific Contact

Prof. Dr. Kálmán Szabó
Forschungszentrum Jülich GmbH
Institute for Advanced Simulation (IAS), Jülich Supercomputing Centre (JSC)
Wilhelm-Johnen-Straße, D-52425 Jülich (Germany)
e-mail: szaboka [@] general.elte.hu

JSC project ID: chfz03

January 2020

Tags: EPP Forschungszentrum Jülich QCD Large-Scale Project