Complex Langevin dynamics and other approaches at finite chemical potential

Abstract

I review the presence of the sign problem in lattice QCD at nonzero baryon density and its relation with the overlap and Silver Blaze problems. I then discuss progress in some cases where the sign problem can be handled, either because the sign problem is absent or because it is milder than in full QCD. Some time is spent on effective three-dimensional models, which can be treated with a variety of methods. I conclude with a discussion of the applicability of complex Langevin dynamics at nonzero density.

22 pages, several figures, invited plenary talk at Lattice 2012, Cairns, Australia, June 24-29 2012; ref [36] properly corrected

References in corpus (23)

• The Complex Langevin method: When can it be trusted?
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential
• Adaptive stepsize and instabilities in complex Langevin dynamics
• Nuclear Physics from lattice QCD at strong coupling
• Towards the phase diagram of dense two-color matter
• The order of the Roberge-Weiss endpoint (finite size transition) in QCD
• A Quarkyonic Phase in Dense Two Color Matter?
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Stability of complex Langevin dynamics in effective models
• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• Singular values of the Dirac operator in dense QCD-like theories
• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Real-time gauge theory simulations from stochastic quantization using optimized updating
• The phase diagram of a gauge theory with fermionic baryons
• Holographic Roberge-Weiss Transitions
• Mean field theory of effective spin models as a baryon fugacity expansion
• The sign problem and the Lefschetz thimble
• Non-relativistic spectrum of two-color QCD at non-zero baryon density
• Temporal breakdown and Borel resummation in the complex Langevin method
• QCD at nonzero temperature and density
• High Temperature QCD

Cited by in corpus (42)

• Approaches to the sign problem in lattice field theory
• Controlling complex Langevin dynamics at finite density
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• Localised distributions and criteria for correctness in complex Langevin dynamics
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Complex saddle points and the sign problem in complex Langevin simulation
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• Reliability of Taylor expansions in QCD
• Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of non-relativistic fermions in one dimension
• Chiral Symmetry Breaking on the Lattice
• Progress in complex Langevin simulations of full QCD at nonzero density
• Tensor renormalization group study of the 3d $O(2)$ model
• New developments for dual methods in lattice field theory at non-zero density
• Controlling the Sign Problem in Finite Density Quantum Field Theory
• The density in the density of states method
• Applying constrained simulations for low temperature lattice QCD at finite baryon chemical potential
• Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Schwinger Mechanism with Stochastic Quantization
• Adaptive gauge cooling for complex Langevin dynamics
• The Discrete Langevin Machine: Bridging the Gap Between Thermodynamic and Neuromorphic Systems
• Confronting effective models for deconfinement in dense quark matter with lattice data
• QCD at nonzero chemical potential: recent progress on the lattice
• Developments in lattice QCD for matter at high temperature and density
• Complex Langevin dynamics for SU(3) gauge theory in the presence of a theta term
• Dual representation for 1+1 dimensional fermions interacting with 3+1 dimensional U(1) gauge fields
• Localised distributions in complex Langevin dynamics
• Hopping parameter expansion to all orders using the complex Langevin equation
• Extending complex Langevin simulations to full QCD at nonzero density
• A short introduction to heavy-ion physics
• Quark-gluon plasma phenomenology from the lattice
• Solving the sign problem of two flavor scalar electrodynamics at finite chemical potential
• On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models
• Curvature of the QCD critical line with 2+1 HISQ fermions
• The Lambert W Function, Laguerre Polynomials, and the Zeros of the QCD Partition Function
• Curvature of the pseudocritical line in (2+1)-flavor QCD with HISQ fermions
• The sign problem and Abelian lattice duality
• Investigating corrections to a Gaussian distribution of the complex phase
• Model studies of the chiral and deconfinement transitions in QCD