Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas

Abstract

Stochastic quantization can potentially be used to simulate theories with a complex action due to a nonzero chemical potential. We study complex Langevin dynamics in the relativistic Bose gas analytically, using a mean field approximation. We concentrate on the region with a Silver Blaze problem and discuss convergence, stability, fixed points, and the severeness of the sign problem. The real distribution satisfying the extended Fokker-Planck equation is constructed and its nonlocal form is explained. Finally, we compare the mean field results in finite volume with the numerical data presented in Ref. [1].

20 pages, 6 eps figures, discussion on the severeness of the sign problem added, to appear in JHEP

References in corpus (11)

• The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density
• Canonical partition function and finite density phase transition in lattice QCD
• Lattice simulations of real-time quantum fields
• The density of states method at non-zero chemical potential
• Stochastic quantization at finite chemical potential
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• Method for simulating O(N) lattice models at finite density
• Complex Langevin Equations and Schwinger-Dyson Equations
• A Random Matrix Study of the QCD Sign Problem
• Random matrix analysis of the QCD sign problem for general topology

Cited by in corpus (48)

• The Complex Langevin method: When can it be trusted?
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Review on novel methods for lattice gauge theories
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Controlling complex Langevin dynamics at finite density
• Introductory lectures on lattice QCD at nonzero baryon number
• Adaptive stepsize and instabilities in complex Langevin dynamics
• QCD Thermodynamics from the Lattice
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Complex Langevin dynamics and zeroes of the fermion determinant
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Stability of complex Langevin dynamics in effective models
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Localised distributions and criteria for correctness in complex Langevin dynamics
• Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution
• Bose-Einstein condensation and Silver Blaze property from the two-loop $\Phi$-derivable approximation
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
• Frontiers of finite temperature lattice QCD
• Phase diagram of the quantum O(2)-model in 2+1 dimensions
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Free energy of the self-interacting relativistic lattice Bose gas at finite density
• Extended Mean Field study of complex ${\varphi }^4$-theory at finite density and temperature
• The sign problem across the QCD phase transition
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Optimisation of complex integration contours at higher order
• The Fluctuations of the Quark Number and of the Chiral Condensate
• The density of states approach for the simulation of finite density quantum field theories
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• New techniques and results for worldline simulations of lattice field theories
• Efficient computations of continuous action densities of states for lattice models
• Approximating Grassmann valued path integrals with radial basis function neural networks
• Combining complex Langevin dynamics with score-based and energy-based diffusion models
• Markovian versus non-Markovian stochastic quantization of a complex-action model