Preparing topologically ordered states by Hamiltonian interpolation

TL;DR

This paper investigates methods to prepare topologically ordered states through Hamiltonian interpolation, analyzing stability and effective models in small systems, with applications to various topological models.

Contribution

It introduces a numerical approach to study the stability of topological state preparation via Hamiltonian interpolation and extends analysis to effective anyon models.

Findings

Prepared states show stability depending on initial Hamiltonian.

Effective Hamiltonian analysis identifies relevant physical processes.

Application to multiple topological models demonstrates method's versatility.

Abstract

We study the preparation of topologically ordered states by interpolating between an initial Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate ground state space. By simulating the dynamics for small systems, we numerically observe a certain stability of the prepared state as a function of the initial Hamiltonian. For small systems or long interpolation times, we argue that the resulting state can be identified by computing suitable effective Hamiltonians. For effective anyon models, this analysis singles out the relevant physical processes and extends the study of the splitting of the topological degeneracy by Bonderson. We illustrate our findings using Kitaev's Majorana chain, effective anyon chains, the toric code and Levin-Wen string-net models.