Ydalia Delgado-Mercado on exploring QCD's phase diagram on the lattice

My name is Ydalia Delgado and I come originally from Peru. I am doing a post-doc in theoretical particle physics at the Karl-Franzens Universität in Graz. I started my undergraduate studies in electronic engineering, but as the time went by I realized that I was always curious about understanding how nature works, and so after 3 years (so long!!) I changed to physics, a decision that I will never regret.

I did my Master at the same university in Lima as part of the high-energy-physics group. During the Master I had the opportunity to work at CERN, the European Research Center for Nuclear Physics, for one of the data-analysis groups of ALICE (A Large Ion Collider Experiment). ALICE is a detector located on the Large Hadron Collider (LHC) ring built to study the physics of matter at extreme conditions. Through the collision of lead ions, accelerated almost to the speed of light, very high temperatures are reached and a new phase of strongly-interacting matter forms. This phase, accessible by ALICE, was present at the beginning of the Universe after the Big Bang. My work at CERN was a great experience, because I was part of a big collaboration and could access data coming from real measurements. However, I was always tempted into doing theoretical physics because one can simulate different models and theories and understand better how particles interact. After my master I did my doctoral studies working on a project related to the phase diagram of strongly-interacting matter using Lattice QCD. I did my PhD at the University of Graz under the supervision of Prof. Dr. Christof Gattringer in collaboration with Prof. Dr. Hans Gerd Evertz from the Technical University of Graz.

At low densities and temperatures, matter is made up of atoms, which are composite objects made up of nucleons surrounded by a cloud of electrons. Electrons are elementary particles, whereas neutrons and protons have smaller constituents called quarks. The interactions among quarks are described by the theory of strong interactions called Quantum Chromo Dynamics (QCD). Although quarks have never been observed as individual particles, their existence has been experimentally tested in the late 60s in e-p scattering and in 1974 with the discovery of the J/Psi meson. This fundamental property of QCD is called confinement. Since QCD was proposed in the 70s by Fritzsch, Gell-Mann and Leutwyler, it has been believed that a phase transition from confined matter to deconfined matter occurs at high temperatures and densities. Evidence of deconfined matter, called quark-gluon plasma, was found at the hadron collider SPS at CERN, and later confirmed at RHIC at BNL. Since then, a lot of effort has been put into the study of the different phases of QCD and the order of the transitions as a function of temperature and density. So far, there has been little progress in the exploration of the phase diagram, we only know with certainty the crossover temperature at zero density and at very small density some results are available. Therefore, the QCD phase diagram is a challenge both theoretically and experimentally.

Lattice QCD is one of the most successful tools to make quantitative predictions of QCD. This method consists of discretizing the 4-dimensional space and time in a hypercubic lattice of finite volume, thus making quantities finite and well-defined. The theory is rewritten in its discretized version, and through Monte Carlo simulations, which most of the time turn out to be computationally very expensive, one can compute different quantities related to the hadron spectrum, study chiral symmetry, and also explore the phase transition from the confined to the deconfined phase of QCD at different temperatures and densities. If the correct discretized version of the QCD Lagrangian has been chosen, in the limit of infinite volume and zero lattice spacing (continuum limit) the lattice results should agree with experimental data. Therefore, it is not only a theoretical but also a technical challenge, to get the correct results in as little amount of time as possible. That is one of the reasons why I like Lattice QCD the most, because for me it has the perfect balance between theory, algorithms and data analysis.

At zero and very small density the Lattice has calculated successfully the temperature at which quarks deconfine. Unfortunately, the lattice can not cope with large densities because of the so-called sign problem. In the Monte Carlo simulation, the exponential of the QCD action is used as a probability weight to generate the field configurations. However, at finite chemical potential the QCD action becomes a complex number, hence it cannot be interpreted as a probability weight any more. To circumvent this problem one can make simulations at zero density and then use a Taylor expansion to extrapolate the results to small densities. But exact results are not available yet, and the finite-density regime is inaccessible to the Lattice. Therefore, there is a need for creativity to invent new methods or try new ways to solve the sign problem of QCD.

I am currently working on a method called the dual representation, where the sign problem can be solved exactly. This method consists of rewriting the theory in terms of new variables such that all terms become real and positive and Monte Carlo simulations are accessible. In order to test this method we have used several models, much simpler than QCD but with some of its properties. Apart from choosing the model, it is also very important to choose the most efficient algorithm used in the Monte Carlo simulation. Therefore we have developed our algorithms, which are generalizations of the worm algorithm developed by Prokof'ev and Svistunov, and successfully we have explored the phase diagram of the different models. Step by step we try to get closer to QCD.

Our results are available in:
Phys.Rev.Lett. 106 (2011) 222001
Nucl.Phys. B862 (2012) 737-750
Comput.Phys.Commun. 183 (2012) 1920-1927
Comput.Phys.Commun. 184 (2013) 1535-1546