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Complex Implications of Translational Invariance in Polymer Field Theory

The behavior of complex-Langevin field-theoretic simulations (CL-FTSs) of polymer liquids is sensitive to the nature of saddle-point field configurations, which are solutions of self-consistent field theory (SCFT). Recent work [Kang et al. Macromolecules 2024, 57, 3850] has shown that SCFT saddle-po...

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Bibliographic Details
Published in:Macromolecules 2024-10, Vol.57 (20), p.9900-9910
Main Authors: Kim, Jaeup U., Matsen, Mark W., Morse, David C., Willis, James D.
Format: Article
Language:English
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Summary:The behavior of complex-Langevin field-theoretic simulations (CL-FTSs) of polymer liquids is sensitive to the nature of saddle-point field configurations, which are solutions of self-consistent field theory (SCFT). Recent work [Kang et al. Macromolecules 2024, 57, 3850] has shown that SCFT saddle-points with real fields are generally not isolated solutions but rather members of a low-dimensional family of continuously connected complex-valued saddle-points sharing the same Hamiltonian value. We show that this behavior is a natural consequence of the analyticity and translational invariance of the Hamiltonian, which together demand its invariance under generalized translations by displacements with complex components. We also present a numerical algorithm that minimizes the deleterious effects of this generalized symmetry on the stability of CL-FTSs.
ISSN:0024-9297
1520-5835
1520-5835
DOI:10.1021/acs.macromol.4c01617