Universität zu Köln

Kumar, Saurabh (2025). Exploring Strong Correlations and Strong Disorder in Fermionic Systems: Independent Investigations. PhD thesis, Universität zu Köln.

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Abstract

Despite significant advancements in condensed matter physics, analyzing strongly interacting and disordered systems presents notable challenges that this thesis aims to address. Divided into two distinct projects, this work investigates strongly interacting fermion systems and strongly disordered fermion systems independently. However, both projects share a commonality in the analytical tool employed: the superbosonization formula introduced in [1, 2]. The first project addresses the lack of methods available for analyzing strongly interacting systems. We develop a general analytical framework based on the bosonization formula [1, 2] within the functional integral approach. As a specific application, we examine the one-dimensional strongly interacting Hubbard model at half-filling. However, we encounter challenges in properly defining the continuum limit in time. Consequently, we incorporate the concept of renormalization, exploring how it can be integrated into the bosonization scheme. We acknowledge that the complete execution of these ideas remains a work in progress, reserved for future research. The second project centers on investigating strongly disordered fermion systems within symmetry class D, as outlined by the Altland-Zirnbauer classification of non-interacting fermions [3]. This research is motivated by the proposal of a novel spontaneous symmetry breaking (SSB) phenomenon in class A [4, 5, 6], and aims to uncover similar phenomena in class D systems. We begin with a general formulation of supersymmetric field theory applied to disordered class D systems, focusing on the strong disorder limit and its implications. To explore the potential for novel spontaneous symmetry breaking in class D, we analyze a specific system: monitored free fermions that exhibit measurement-induced phase transitions. We propose a reformulation of the theory that provides a new perspective on investigating this system. Nevertheless, a complete investigation of the possibility of novel SSB phenomena in class D remains an open question for future exploration.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Kumar, Saurabh saurabh97kum@gmail.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-753082
Date:	26 February 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 Bosonization English Strongly interacting fermionic system English Strongly disordered fermionic system English Novel spontaneous symmetry breaking English Measurement-induced phase transition English Superbosonization English
Date of oral exam:	19 December 2024
Referee:	Name Academic Title Zirnbauer, Martin Prof. Dr. Diehl, Sebastian Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/75308