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

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arxiv 0810.2089 v2 pith:25FY5YAK submitted 2008-10-12 hep-lat cond-mat.otherhep-phnucl-th

classification hep-latcond-mat.otherhep-phnucl-th
keywords chemicalpotentialproblemsignfinitequantizationstochasticbose
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lefschetz thimble-inspired weight regularizations for complex Langevin simulations

    hep-lat 2024-12 conditional novelty 7.0 of 10

    A single compact Lefschetz thimble restores correct complex Langevin convergence, and a Dyson-Schwinger bias correction recovers the original expectation values.

  2. Diffusion models learn distributions generated by complex Langevin dynamics

    hep-lat 2024-12 conditional novelty 6.0 of 10

    Diffusion models reproduce the distributions sampled by complex Langevin dynamics in a Gaussian and a quartic toy model with complex mass.

  3. Combining complex Langevin dynamics with score-based and energy-based diffusion models

    hep-lat 2025-10 conditional novelty 5.0 of 10

    Energy-based diffusion models trained on complex Langevin data produce an explicit energy function for the sampled distribution, enabling MCMC without re-simulation.

  4. Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature

    hep-lat 2025-09 conditional novelty 4.0 of 10

    Configurational temperature from action gradients and Hessians offers a sensitive new correctness diagnostic for complex Langevin simulations, reproducing input temperature to 0.2-3% in 1D PT-symmetric models.

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