An Improved Nonperturbative Method for Studying Two-dimensional Vortex Liquids

TL;DR

This paper introduces an enhanced nonperturbative method for analyzing two-dimensional vortex liquids, improving the accuracy of thermal fluctuation effects in high-temperature superconductors by including additional Feynman diagrams.

Contribution

The authors develop a systematic improvement to the parquet approximation by incorporating an infinite subset of diagrams, leading to better resolution of structural features in vortex liquids.

Findings

More pronounced crystalline order observed in the improved model.

Resolution of second and third peaks in the structure factor.

Enhanced understanding of vortex liquid structure in superconductors.

Abstract

We show how a systematic improvement can be made on the nonperturbative parquet approximation method which was previously used to study the effect of thermal fluctuations in vortex liquids in high-temperature superconductors. This is achieved by including an infinite subset of Feynman diagrams contributing to the renormalized four-point vertex function of the Ginzburg-Landau model, which was omitted in the original approximation. We find that the growing crystalline order in the vortex liquid is more pronounced in the improved approximation. In particular, the second and third peaks in the liquid structure factor, which appeared as one peak in the original approximation, are now resolved.