# Thermodynamics with Overlap Fermions

**Principal Investigator:** Balint Toth, Institut für Theoretische Teilchenphysik, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal (Germany)

**HPC Platform:** JUQUEEN of JSC

**Date published: **April 2018

**Project-ID @ JSC:** hwu26

The Universe soon after the Big Bang was hot and full of massless particles, so called fermions and bosons. As it expanded and cooled down particles become massive. They acquired mass from several kinds of mechanisms, which are investigated in detail in heavy-ion collision experiments, and also in theory. Ab-initio theoretical calculations require simulating massless particles on a supercomputer. This is a difficult problem, fortunately with an existing solution, the so-called overlap discretization of fermions.

Simulations with overlap fermions is an expensive endeavour in terms of computer time. One can turn to alternative fermion discretisations, which are much cheaper but give up the concept of massless particles. For many physical problems, such as calculating the energy density and pressure of the early Universe, these cheap variants provide a cost-effective and even theoretically justifiable approach. There are a few physical phenomena though, where starting from zero mass particles is crucial. One such problem is calculating how a certain quantity, called topology, fluctuates in the hot Universe. These calculations provide important input for searching for dark matter particles. Massless fermions suppress these fluctuations, massive fermions don't.

In order to determine the correct value of these fluctuations, overlap fermions are the method of choice. One might try measurements with the cheaper fermion alternatives, but in the end they turn out way more expensive. This is demonstrated on Figure 1, which on the x-axis shows the inverse size of the lattice (the smaller the more expensive), on the y-axis the suppression of the fluctuations (the result of the calculation). The red and green points are obtained with two variants of the cheap fermion formulations, the blue ones with overlap fermions. Overlap fermions yield a result, which is independent of the lattice size. The cheaper formulations change rapidly, and would require gigantic lattices to reach the same result as with overlap fermions.

The simulations were carried out on JUQUEEN, by an international team of researchers in Wuppertal and Budapest. The Wuppertal efforts of the overlap fermion simulations were coordinated by Balint Toth.

Copyright: University of Wuppertal

**Scientific Contact:**

Dr. Balint Toth

Institut für Theoretische Teilchenphysik

Fakultät für Mathematik und Naturwissenschaften

Bergische Universität Wuppertal, D-42097 Wuppertal (Germany)

e-mail: btoth [@] uni-wuppertal.de

April 2018

Project ID: *hwu26*