Thermal QCD on the lattice – from finite density to non-uniform magnetic fields

The first microseconds of the universe were characterized by a hot and dense soup of strongly interacting quarks and gluons. Nowadays, HIC experiments attempt to recreate the conditions of the early universe to study how these interactions come about at high temperatures ($T$), baryon chemical potentials (μ_B), and magnetic fields ($B$). Moreover, theoretical predictions indicate that magnetic fields in HICs are not only strong but also highly inhomogeneous in space. Using state-of-the-art computer simulations of the underlying theory, Quantum Chromodynamics (QCD), discretized on a lattice, we have increasingly deepened our knowledge of strong-interaction physics from first principles. In this work, we studied various aspects of QCD using the lattice approach, with particular focus on the impact of μ_B and inhomogeneous $B$ on QCD observables. To this end, we employed $2+1$ and $2+1+1$ flavors of staggered fermions with physical masses, and the tree-level Symanzik-improved gauge action. Our results are divided into three parts: in part (1), we studied the interplay between μ_B and non-zero $B$ in the light of the Equation of State (EoS) of QCD via Taylor expansion to circumvent the sign problem. We determined the $T$ and $B$ dependence of the Leading Order (LO) contribution to the EoS in the presence of strangeness-neutrality and isospin-asymmetry constraints, which are relevant in phenomenological studies of HICs. In part (2), we computed the approximate order parameters of chiral and deconfinement transitions -- the chiral condensate and the Polyakov loop -- in the presence of an inhomogeneous magnetic background. We showed that, in this scenario, these observables manifest novel localized features. Finally, we extrapolated the results to the continuum limit. In part (3), we demonstrated that the field induces a local electric current density in the equilibrated medium. We also introduced a new approximation technique -- based on a resummation of $B$-dependent expectation values into so-called sea and valence contributions -- to extract information about the medium properties, such as the magnetic susceptibility, at a lower computational cost. Our continuum-extrapolated results for the magnetic susceptibility corroborate the existence of at least two magnetic phases in QCD: a strong paramagnetic phase at high $T$, and a weak diamagnetic phase at low $T$. Finally, we advocate that our approximation technique may be relevant in studies involving more computationally expensive actions, e.g. Wilson, overlap, and domain-wall fermions, in the presence of magnetic fields.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bielefeld

Year

2025

Author dc:creator

• Marques Valois, Adeilton Dean

Repository record source_url

https://pub.uni-bielefeld.de/record/3006059

OAI identifier oai:identifier

oai:pub.uni-bielefeld.de:3006059