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 (6)

• Canonical partition function and finite density phase transition in lattice QCD
• Lattice simulations of real-time quantum fields
• 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

Cited by in corpus (3)

• QCD Thermodynamics from the Lattice
• Random matrix analysis of the QCD sign problem for general topology
• Two complex problems on the lattice: transport coefficients and finite chemical potential