Monopole-Enriched Groundstates of Two-Dimensional BCS Models

TL;DR

This paper analyzes the groundstate sectors of two-dimensional Bose-condensed BCS models with magnetic flux, linking their macroscopic properties to the moduli space of solutions to the Gross-Pitaevskii equations on complex bundles.

Contribution

It introduces a novel approach to characterize groundstates via the moduli space of gauge-inequivalent solutions to the Gross-Pitaevskii equations in 2D BCS models.

Findings

Identifies the groundstate sectors using moduli space analysis.

Connects physical properties to solutions of nonlinear equations on fiber bundles.

Provides a framework inspired by topological order and fractionalization theories.

Abstract

We extract the macroscopic characteristics of the groundstate sectors of two dimensional Bose-condensed BCS models with a fixed number of magnetic flux quanta, on length scales much larger than the characteristic size of the Cooper-pair bound states. We show that this reduces to the problem of computing the moduli space of gauge-inequivalent solutions to the Gross-Pitaevskii equations on a nontrivial fibre bundle. Inspired in part by the physical arguments of Oshikawa and Senthil in Fractionalization, Topological Order, and Quasiparticle Statistics, we extract a large class of groundstates from this moduli space.