Complex Langevin simulations and the QCD phase diagram: recent developments

Abstract

In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here we focus on the explicit computation of boundary terms, which provide an observable that can be used to check one of the criteria of correctness explicitly. We also present the method of Dynamic Stabilization and elaborate on recent results for fully dynamical QCD.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

“…For a review of the equation of state relating to heavy ion phenomenology, see [81,82]. Note also, that this low density regime appears to be accessible by complex Langevin simulations without recourse to series expansions, albeit not yet for physical quark masses [83]. This offers an additional cross check between different methods.…”

QCD at high temperature and density: selected highlights

“…In the following only a few selected highlights will be presented. Complex Langevin methods have now reached the point where they have been used to simulate fully dynamical QCD with pion masses down to ⇠ 500 MeV [49][50][51]. Figure 3 shows the fermion density as a function of the chemical potential from a simulation with N f = 2 Wilson fermions with m ⇡ ⇡ 500 MeV and a lattice spacing a ⇡ 0.06 fm [51].…”

Stable solvers for real-time Complex Langevin

“…[1] for a mini-review) remains one of the central open challenges in modern theoretical physics and hinders progress in various different subfields. It underlies the challenges encountered in the study of transport properties of the quarkgluon-plasma [2][3][4][5][6][7][8][9], it is the central hurdle in the exploration of the QCD phase diagram at large Baryon density [10][11][12][13][14][15] and impacts the study of the thermodynamics of imbalanced Fermi gases [16][17][18], to name just three. The term sign problem refers to the fact that many strongly correlated quantum systems of phenomenological relevance can only be expressed through a path integral with complex valued Feynman weight.…”

“…The stability and regularization properties of the implicit schemes offer benefits in other applications of complex Langevin beyond real-time simulations, such as the treatment of strongly interacting systems at finite chemical potential (for a recent review on CL and the QCD phase diagram see e.g. [15]).…”