# Exceptional points preceding and enabling spontaneous symmetry breaking

## TL;DR

This paper explores how symmetry breaking and exceptional points relate in nonlinear optical systems, finding they often occur separately but are still connected.

## Contribution

The paper reveals that symmetry breaking and specific exceptional points do not always coincide, challenging previous assumptions.

## Key findings

- Symmetry breaking and exceptional points occur at different points in parameter space.
- The relationship between the two phenomena is interdependent but not coincident.
- This behavior is consistent across multiple optical systems, suggesting a general principle.

## Abstract

Spontaneous symmetry breaking (SSB) plays a central role in many areas of physics, from particle interactions to optical systems. Exceptional points (EPs), where system properties become degenerate, are often believed to occur together with SSB. Here we investigate the intricate relationship between SSB and a specific class of EPs across three distinct, real-world scenarios in nonlinear optics. In these systems, the two phenomena do not coincide; they occur at dislocated points in parameter space, but are interdependent. This recurring behavior across disparate platforms implies that such decoupling is not unique to these optical systems, but likely reflects a more general principle. Our results highlight the need for careful analysis of assumed correlations between SSB and EPs in both theoretical and applied contexts. They deepen our understanding of nonlinear dynamics in optical systems and prompt a broader reconsideration of contexts where EPs and SSB are thought to be interdependent.

Symmetry breaking is often assumed to coincide with underlying exceptional points. The authors show that certain Jacobian-derived subsets instead occur as precursors, highlighting the need to identify the correct exceptional points when predicting specific symmetry-breaking transitions.