# Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases

## TL;DR

This paper introduces a novel perspective on entanglement entropy in topological phases by relating it to quasiparticle fluctuations, thermal entropy, and explicit computations in quantum double models with boundaries.

## Contribution

It presents a new approach linking entanglement spectrum to quasiparticle fluctuations and constructs reduced density matrices for quantum double models on various 2-surfaces.

## Key findings

- Entanglement entropy equals the maximal quasiparticle fluctuations on the entanglement boundary.
- Entanglement entropy corresponds to the thermal entropy of quasiparticles at infinite temperature.
- Explicit computations validate the theoretical framework in quantum double models with boundaries.

## Abstract

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system is identified with the spectrum of quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries.