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Complex Langevin and other approaches to the sign problem in quantum many-body physics

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arxiv 1907.10183 v2 pith:ZZMRY3IM submitted 2019-07-24 cond-mat.quant-gas hep-latnucl-th

Casey E. Berger , Lukas Rammelmüller , Andrew C. Loheac , Florian Ehmann , Jens Braun , Joaquín E. Drut This is my paper · ORCID
classification cond-mat.quant-gashep-latnucl-th
keywords complexquantumproblemapplicationsapproachescasefermionslangevin
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We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard-Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.

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Cited by 3 Pith papers

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  1. Stochastic Quantization as Optimal Control

    hep-lat 2026-07 conditional novelty 6.0 of 10

    Stochastic quantization is re-expressed as finite-time optimal control, in which a learned Doob force plus exact path weights reach the Gibbs measure without waiting for equilibrium.

  2. 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.

  3. Dense and magnetized QCD from imaginary chemical potential

    hep-lat 2025-02 conditional novelty 4.0 of 10

    First 2+1+1 flavor lattice QCD results for the leading-order dense QCD equation of state in a magnetic field, along the strangeness-neutral, isospin-asymmetric trajectory, suggesting strong magnetic effects near the c...

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