Coherent States Formulation of Polymer Field Theory

TL;DR

This paper presents a novel complex Langevin simulation scheme for the coherent-states formulation of polymer field theory, offering a more explicit and potentially versatile alternative to traditional auxiliary-field methods.

Contribution

It introduces a stable, efficient CL scheme for the CS formulation, which avoids non-linear, non-local functionals and simplifies numerical simulations of polymer systems.

Findings

CS-CL results agree with standard AF simulations

The formalism is applicable to various polymer architectures

Potential for improved coarse-graining and renormalization-group studies

Abstract

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.