Models for the BPS Berry Connection

TL;DR

This paper introduces a systematic method to construct quantum models where the Berry connection mimics the BPS monopole, using a single arbitrary function to generate infinitely many such models.

Contribution

It provides a novel systematic construction of Schrödinger Hamiltonians with Berry connections equivalent to BPS monopoles, expanding the class of models simulating monopole physics.

Findings

Constructed infinitely many quantum models with BPS monopole Berry connections.

Demonstrated the role of a single arbitrary monotonic function in model generation.

Connected quantum mechanical models to classical monopole solutions.

Abstract

Motivated by the Nahm's construction, in this paper we present a systematic construction of Schr\"{o}dinger Hamiltonians for a spin-1/2 particle where the Berry connection in the ground-state sector becomes the Bogomolny-Prasad-Sommerfield (BPS) monopole of $SU(2)$ Yang-Mills-Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.