# Choreographed entangle dances: topological states of quantum matter

## TL;DR

This paper explores topological states of quantum matter at zero temperature, highlighting their unique entanglement properties and significance in unifying fundamental concepts in physics.

## Contribution

It introduces the concept of topological phases in quantum matter, emphasizing states with topological and SPT order that do not involve symmetry breaking.

## Key findings

- Topological phases can exist without symmetry breaking.
- Quantum matter can have highly entangled topological order.
- Emergent properties unify fundamental physical concepts.

## Abstract

For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at zero temperature, even symmetric disordered liquids can have features, which give rise to topological phases of quantum matter. Some of the topological phases are highly entangled (i.e. have topological order), while others are weakly entangled (i.e. have SPT order). In this article, we will briefly introduce those new zero-temperature states of matter and their amazing emergent properties. We will also discuss their significance in unifying some most basic concepts in nature.