Nudging Quantum Matter over the Edge of Topological Order

Benjamin Michen

AutorIn

Benjamin Michen

Titel

Nudging Quantum Matter over the Edge of Topological Order

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-1045175

Auflage

Erstveröffentlichung

2026

Datum der Einreichung

20.11.2025

Datum der Verteidigung

01.04.2026

Abstract (EN)

This thesis explores multiple ways of nudging quantum matter over the edge of topological order and is divided into two parts. The first part offers an overview of the theoretical foundations for the original results presented in the second part. These results first focus on non-standard dynamical paths between trivial and topological phases with applications to adiabatic state preparation in atomic quantum simulators. We commence with the adiabatic preparation of a fractional Chern insulator from a one-dimensional charge density wave. To achieve this, we show analytically how an anisotropy of the hopping amplitudes can effectively change the aspect ratio of the system and induce a so-called ``thin-torus'' limit. The analytical results are corroborated using numerical exact diagonalization. Subsequently, we investigate the adiabatic preparation of a number-conserving Majorana phase protected by a parity symmetry that emerges at a critical point of a two-leg ladder subject to a pair-hopping interaction. For this purpose, we design a symmetry-breaking flux term that can gap out the critical target state and devise a protocol that ramps down the flux term with a power law adapted to system size so as to enable an optimal (linear) scaling of preparation time. To design the flux term, we treat the system in the framework of constructive bosonization. The results are supported numerically using matrix product state techniques to calculate excitation gaps, correlation functions, and time evolutions. Then, we shift the focus to the identification of minimal requirements for topological effects and demonstrate how an integer quantum Hall phase can form in a topologically completely trivial band structure at the onset of disorder. These results are confirmed through extensive numerical simulations with the software package Kwant. Finally, we investigate a Floquet system in an anomalous topological phase that is subjected to nonlinear effects. Specifically, we demonstrate a nonlinearity induced scattering of an edge state off a circulating bulk mode by calculating the exact dynamics of the system through a numerical solution of the nonlinear Schrödinger equation. Notably, we find that the scattering amplitude is determined by interference effects between the two pulses and therefore highly sensitive to their initial relative phase.

Freie Schlagwörter (EN)

Topology, Many-Body-Theory

Klassifikation (DDC)

530

Klassifikation (RVK)

UK 1000

GutachterIn