Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential

Abstract

A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and `Silver Blaze' problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. Independence of chemical potential at small and a transition to a condensed phase at large chemical potential are found. Lattices of size N^4, with N=4,6,8,10, are used. We show that the sign problem is severe, however, we find that it has no negative effect using this approach. This improves the prospects of applying stochastic quantization to QCD at nonzero density.

4 pages, 4 eps figures, v2: minor changes, outlook expanded, references added, to appear in PRL

References in corpus (25)

• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• QCD at finite isospin density
• Finite density QCD via imaginary chemical potential
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• A new method to study lattice QCD at finite temperature and chemical potential
• The Equation of State for Two Flavor QCD at Non-zero Chemical Potential
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• 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
• Functional integrals for QCD at nonzero chemical potential and zero density
• Pressure and non-linear susceptibilities in QCD at finite chemical potentials
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• The QCD equation of state at nonzero densities: lattice result
• Lattice simulations of real-time quantum fields
• The density of states method at non-zero chemical potential
• Stochastic quantization at finite chemical potential
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Simulating nonequilibrium quantum fields with stochastic quantization techniques
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Chiral Symmetry Breaking and the Dirac Spectrum 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

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