Universität zu Köln

Contessi, Daniele ORCID: 0000-0002-2610-8496 (2023). Data driven approach to detection of quantum phase transitions. PhD thesis, Universität zu Köln.

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Abstract

Phase transitions are fundamental phenomena in (quantum) many-body systems. They are associated with changes in the macroscopic physical properties of the system in response to the alteration in the conditions controlled by one or more parameters, like temperature or coupling constants. Quantum phase transitions are particularly intriguing as they reveal new insights into the fundamental nature of matter and the laws of physics. The study of phase transitions in such systems is crucial in aiding our understanding of how materials behave in extreme conditions, which are difficult to replicate in laboratory, and also the behaviour of exotic states of matter with unique and potentially useful properties like superconductors and superfluids. Moreover, this understanding has other practical applications and can lead to the development of new materials with specific properties or more efficient technologies, such as quantum computers. Hence, detecting the transition point from one phase of matter to another and constructing the corresponding phase diagram is of great importance for examining many-body systems and predicting their response to external perturbations. Traditionally, phase transitions have been identified either through analytical methods like mean field theory or numerical simulations. The pinpointing of the critical value normally involves the measure of specific quantities such as local observables, correlation functions, energy gaps, etc. reflecting the changes in the physics through the transition. However, the latter approach requires prior knowledge of the system to calculate the order parameter of the transition, which is uniquely associated to its universality class. Recently, another method has gained more and more attention in the physics community. By using raw and very general representative data of the system, one can resort to machine learning techniques to distinguish among patterns within the data belonging to different phases. The relevance of these techniques is rooted in the ability of a properly trained machine to efficiently process complex data for the sake of pursuing classification tasks, pattern recognition, generating brand new data and even developing decision processes. The aim of this thesis is to explore phase transitions from this new and promising data-centric perspective. On the one hand, our work is focused on the development of new machine learning architectures using state-of-the-art and interpretable models. On the other hand, we are interested in the study of the various possible data which can be fed to the artificial intelligence model for the mapping of a quantum many-body system phase diagram. Our analysis is supported by numerical examples obtained via matrix-product-states (MPS) simulations for several one-dimensional zero-temperature systems on a lattice such as the XXZ model, the Extended Bose-Hubbard model (EBH) and the two-species Bose Hubbard model (BH2S).

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Contessi, Daniele daniele@contessi.net orcid.org/0000-0002-2610-8496 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-715622
Date:	19 July 2023
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 Quantum many-body systems English Concrete Autoencoder English Entanglement Spectrum English Full Counting Statistics English Phase diagram English Machine Learning English Tensor Network English Phase transitions English Generative Adversarial Network (GAN) English
Date of oral exam:	19 July 2023
Referee:	Name Academic Title Trebst, Simon Prof. Nieuwenburg, Evert P. L. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/71562