# Intertwined Topological Phases induced by Emergent Symmetry Protection

## TL;DR

This paper uncovers a new mechanism where emergent symmetry protection in strongly correlated systems leads to intertwined topological phases, revealing novel static and dynamic phenomena.

## Contribution

It introduces a novel mechanism for symmetry protection emerging from broken symmetries, leading to intertwined topological phases in strongly correlated systems.

## Key findings

- Emergent symmetry protection arises dynamically from broken symmetries.
- Intertwined topological phases coexist with long-range order.
- Interaction-induced topological phase transitions and fractional pumping are observed.

## Abstract

The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges dynamically from a set of configurations enforced by another broken symmetry. This novel mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.