Complex Self-Consistent Field Theory: A Hidden Symmetry of Polymer Field Theory

Abstract

Self-consistent field theory (SCFT) is a theoretical tool employed to determine the mean field solution of heterogeneous polymer systems. Thus, it has been naturally assumed that the fields and ensemble average densities in SCFT solutions are real-valued functions. However, our current investigation challenges this presumption, revealing a possibility that the saddle point approximation leading to the SCFT solution may result in complex-valued solutions. Focusing on A and B homopolymer mixture and AB diblock copolymers, we explore the conditions for obtaining such saddle points and find that the fields consistently manifest as Hermitian functions when there are nonvanishing imaginary parts, resembling the PT symmetric system in quantum mechanics. This intriguing revelation holds significance as it contributes to a deeper understanding of complex Langevin field theoretic simulations, wherein such complex solutions are frequently encountered.