# Decoherence and relaxation of topological states in extended quantum Ising models

## TL;DR

This paper investigates how topological states in extended quantum Ising models decohere and relax due to environmental interactions, focusing on the relation between these processes and the system's topological properties.

## Contribution

It derives a Lindblad equation for many-body states and analyzes decoherence and relaxation in topological phases of extended quantum Ising chains.

## Key findings

- Dephasing rates are analyzed in topological phases at low temperature.
- The relation between decoherence, energy relaxation, and topology is elucidated.
- The study provides insights into the stability of topological states under environmental noise.

## Abstract

We study the decoherence and the relaxation dynamics of topological states in an extended class of quantum Ising chains which can present a manyfold ground state subspace. The leading interaction of the spins with the environment is assumed to be the local fluctuations of the transverse magnetic field. By deriving the Lindblad equation using the many-body states, we investigate the relation between decoherence, energy relaxation and topology. In particular, in the topological phase and at low temperature, we analyze the dephasing rates between the different degenerate ground states.