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.

arXiv comment7 pages, 1 figure, 4 tables, to appear in EPJA

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• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• What neutron stars tell about the hadron-quark phase transition: a Bayesian study
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations
• NNLO HTLpt predictions for the curvature of the QCD phase transition line
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Stable solvers for real-time Complex Langevin
• Simulating Yang-Mills theories with a complex coupling
• Pairing patterns in polarized unitary Fermi gases above the superfluid transition
• Real-time correlators in 3+1D thermal lattice gauge theory
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• Towards sampling complex actions
• Regularization of Complex Langevin Method
• Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density
• A lattice pairing-field approach to ultracold Fermi gases
• QCD at high temperature and density: selected highlights