Complex Langevin: correctness criteria, boundary terms, and spectrum
The Complex Langevin (CL) method to simulate “complex probabilities” ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex “probability” measure. The situation may be spoiled in two ways: failure to converg...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 January 2024
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| In: |
Physical review
Year: 2024, Volume: 109, Issue: 1, Pages: 1-13 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.109.014509 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1103/PhysRevD.109.014509 Verlag, kostenfrei, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.109.014509 
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| Author Notes: | Erhard Seiler, Dénes Sexty, and Ion-Olimpiu Stamatescu |
| Summary: | The Complex Langevin (CL) method to simulate “complex probabilities” ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex “probability” measure. The situation may be spoiled in two ways: failure to converge and convergence to the wrong limit. It was found long ago that “wrong convergence” is caused by boundary terms; nonconvergence may arise from bad spectral properties of the various evolution operators related to the CL process. Here, we propose a class of criteria that allow one to rule out boundary terms and at the same time bad spectrum. Ruling out boundary terms in the equilibrium distribution arising from a CL simulation implies that the so-called convergence conditions are fulfilled. This in turn has been shown to guarantee that the expectation values of holomorphic observables are given by complex linear combinations of exp(−𝑆) over various integration cycles. If the spectrum is pathological, however, the CL simulation in general does not reproduce the integral over the desired real cycle. |
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| Item Description: | Veröffentlicht: 24. Januar 2024 Gesehen am 19.07.2024 |
| Physical Description: | Online Resource |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.109.014509 |