# Goldstone modes in the emergent gauge fields of a frustrated magnet

## TL;DR

This paper investigates Goldstone modes in the emergent gauge fields of a frustrated magnet's spin-glass phase, revealing that these modes are excitations of U(1) gauge fields and require a modified theoretical description.

## Contribution

It demonstrates that Goldstone modes in a frustrated magnet's spin-glass phase are gauge field excitations, extending the standard theory for Heisenberg spin glasses.

## Key findings

- Goldstone modes are excitations of emergent U(1) gauge fields.
- Standard Goldstone mode theory needs modification in this context.
- The system exhibits three copies of gauge fields related by spin-rotation symmetry.

## Abstract

We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.