Status of Complex Langevin

Abstract

I review the status of the Complex Langevin method, which was invented to make simulations of models with complex action feasible. I discuss the mathematical justification of the procedure, as well as its limitations and open questions. Various pragmatic measures for dealing with the existing problems are described. Finally I report on the progress in the application of the method to QCD, with the goal of determining the phase diagram of QCD as a function of temperature and baryonic chemical potential.

Plenary talk given at Lattice 2017, Granada; 21 pages, 14 figures; a reference added, some more typos corrected

References in corpus (7)

• Toward solving the sign problem with path optimization method
• Complex Langevin dynamics and zeroes of the fermion determinant
• Does the complex Langevin method give unbiased results?
• Reweighting complex Langevin trajectories
• Exploring the phase diagram of QCD with complex Langevin simulations
• Testing dynamic stabilisation in complex Langevin simulations
• Complex Langevin in Lattice QCD: dynamic stabilisation and the phase diagram

Cited by in corpus (30)

• Review on novel methods for lattice gauge theories
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin and boundary terms
• Dense 2-color QCD towards continuum and chiral limits
• Controlling Complex Langevin simulations of lattice models by boundary term analysis
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Applying Complex Langevin Simulations to Lattice QCD at Finite Density
• Finite-density gauge correlation functions in QC2D
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Testing the criterion for correct convergence in the complex Langevin method
• Towards learning optimized kernels for complex Langevin
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Stable solvers for real-time Complex Langevin
• Functional renormalization group study of the critical region of the quark-meson model with vector interactions
• Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2+1) Polyakov-Nambu-Jona-Lasinio Model
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Dual simulation of a Polyakov loop model at finite baryon density: phase diagram and local observables
• Schwinger-Dyson equations and line integrals
• Complex Langevin approach to interacting Bose gases
• Beyond Complex Langevin Equations: positive representation of a class of complex measures
• Towards sampling complex actions
• Representation of complex probabilities and complex Gibbs sampling
• Positive representations of complex distributions on groups
• Explicit positive representation for weights on $R^d$
• Satisfying positivity requirement in the Beyond Complex Langevin approach
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density
• A lattice pairing-field approach to ultracold Fermi gases
• On the validity of complex Langevin method for path integral computations
• Beyond Complex Langevin Equations: a Progress Report
• Complex Langevin for Lattice QCD