Complex Langevin: Correctness criteria, boundary terms and spectrum
| Autor: | Seiler, Erhard, Sexty, Dénes, Stamatescu, Ion-Olimpiu |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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; non-convergence may arise from bad spectral properties of the various evolution operators related to the CL process, and is also signalled by boundary terms, although superficially they may seem unrelated. Here we propose a class of criteria which allow to rule out boundary terms and at the same time bad spectrum. It turns out, however, that the two phenomena are not strictly related: while there is a regime in which the criteria are satisfied and the spectrum is good, there is also an intermediate regime in which the criteria are violated, boundary terms are present, leading to wrong convergence of CL, yet the spectrum still looks good. This shows that the absence of boundary terms is crucial for correctness, wheres the spectrum plays only a subsidiary role. Comment: 25 pages, 8 figures |
| Databáze: | arXiv |
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