Universität zu Köln

Weerda, Erik Lennart (2025). Quantum Matter and Tensor Networks in Two Dimensions. PhD thesis, Universität zu Köln.

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Abstract

The numerical study of quantum matter in two dimensions plays an important role in both conventional condensed matter systems and cold atom experiments. In this thesis, we explore the use of two-dimensional tensor networks — specifically, tensor product states — for this task. These states are alternatively referred to as projected entangled pair states. We present complementary results of methodological advances for tensor product states, together with applications of these states in both finite and infinite lattice systems. On the methodological side, we introduce an accurate and computationally efficient algorithm for the contractions of the relevant two-dimensional tensor networks alongside practical schemes to achieve more efficient optimization of tensor product states. Additionally, we apply the methods of two-dimensional tensor networks to models describing several physical situations, including spin systems, Josephson junction arrays, the bosonic Harper-Hofstader model relevant for cold-atom platforms with synthetic gauge fields, as well as Rydberg atom arrays. The results of this thesis thus contribute to demonstrating and improving the versatility of tensor product states as a framework for addressing complex questions in two-dimensional quantum matter.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Weerda, Erik Lennart erik.weerda@outlook.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-793487
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 Tensor Networks English
Date of oral exam:	15 September 2025
Referee:	Name Academic Title Rizzi, Matteo Prof. Dr. Kugler, Fabian Jun.-Prof. Dr
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79348