Universität zu Köln

Tausendpfund, Niklas ORCID: 0000-0002-7167-3793 (2025). On the Design and Characterization of Exotic Phases in One Dimension. PhD thesis, Universität zu Köln.

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Abstract

State-of-the-art quantum simulators -- ranging from ultracold atoms and trapped ions to Rydberg arrays and superconducting qubits -- have rapidly evolved into powerful platforms for investigating complex quantum many-body phenomena. In this thesis, we discuss various models and their static and non-equilibrium properties that can be realized on near-term quantum devices. We conduct comprehensive studies on the phases of these models, spanning novel symmetry-protected topological and critical gapless phases in one dimension to the non-equilibrium behavior of localized excitations in one-dimensional quantum chains and extended one-dimensional quantum objects embedded in a two-dimensional quantum magnet. On the technical side, we employ extensive tensor network simulations to validate our findings and introduce new algorithms to determine the lifetime of edge excitations emerging in the symmetry-protected topological phase of fermionic chains. Furthermore, we propose a new variational ansatz to directly search for these novel edge modes in the topological phase. By integrating analytical tools and tensor network simulations, this thesis contributes to the roadmap for establishing quantum simulators as promising tools for investigating complex quantum systems.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Tausendpfund, Niklas niklastausendpfund@protonmail.com https://orcid.org/0000-0002-7167-3793 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-790553
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language One-Dimensional Systems English Quantum Many-Body Systems English Majorana Zero Modes English Almost Strong Zero Modes English Tricritical Ising Model English Domain Wall Dynamics English Tensor Networks English Matrix Product States English
Date of oral exam:	8 October 2025
Referee:	Name Academic Title Rizzi, Matteo Prof. Dr. Rosch, Achim Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79055