# Hopfions in lattice dimer model

## TL;DR

This paper investigates topological properties of 3D lattice dimer models, revealing the existence of Hopfion defects characterized by the Hopf invariant, and proposes their potential realization in spin ice materials.

## Contribution

It provides an explicit algebraic expression for Hopf invariants in lattice dimer models and classifies their topological states, linking to spin ice systems.

## Key findings

- Identification of topological defects as Hopfions
- Explicit algebraic expression for Hopf invariant in dimer models
- Proposal to search for hopfions in spin ice materials

## Abstract

In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit algebraic expression in terms of effective magnetic field of a dimer configuration. Thus, we solve the problem of topological classification of possible states in 3D lattice dimer model. Furthermore, since the lattice dimer model is known to be dual to spin ice, our work can be viewed as a proposal to search for hopfions in classical, as well as, artificial spin ice and related materials.