CENTRA Seminar - Diagrammatic methods for strongly-coupled lattice QCD at finite temperature and density - 27 julho 2017

We start by motivating the use of lattice and Monte Carlo methods to study the physical properties of Quantum Chromodynamics (QCD) at non-zero temperature and non-zero baryon density. This system, however, is plagued by the so-called "sign problem", which renders "ab initio" numerical simulations impractical. We summarise the most popular approaches to tackle the sign problem in lattice QCD. In particular, we focus on the diagrammatic approach at strong coupling, and on the efficient generation of important diagrams using worm algorithms. 

 

 

We show how to compute physical observables in diagrammatic QCD, directly in the chiral limit, and in particular we present the full phase diagram of lattice QCD in the strong coupling limit. We also propose a simple criterion for the non-perturbative renormalisation of a bare coupling of the theory, which significantly improves the precision of physical results in the continuum time limit. If time permits: we present our results on the equation of state of lattice QCD at zero chemical potential, and how it compares to the Stefan-Boltzmann law of a free pion gas; extensions of the diagrammatic approach beyond the strong coupling limit are also touched briefly.