Instantons and Berry's connections on quantum graph

TL;DR

This paper explores the relationship between instanton solutions and Berry's connections in quantum graphs, revealing that instantons manifest as Berry's connections through the application of the ADHM construction.

Contribution

It introduces a novel approach by applying the ADHM construction to analyze non-Abelian Berry's connections on quantum graphs, linking instantons with Berry's phases.

Findings

Instanton configurations are realized as Berry's connections.

The ADHM construction effectively models Berry's connections on quantum graphs.

Non-Abelian Berry's connections can be characterized by instanton solutions.

Abstract

In this paper, we study non-Abelian Berry's connections in the parameter space of boundary conditions for Dirac zero modes on quantum graphs. We apply the ADHM construction, which is the method for constructing Yang-Mills instanton solutions, to the Berry's connections. Then we find that the instanton configurations appear as the Berry's connections.