Public defence in Engineering Physics, M.Sc. Pascal Vecsei
Public defence from the Aalto University School of Science, Department of Applied Physics.
Title of the thesis: Detection of Quantum Phase Transitions with a Lee-Yang Formalism and Many-Body Algorithms
Doctoral student: Pascal Vecsei
Opponent: Professori Cristiane Morais-Smith, Utrech University, Netherlands
Custos: Assistant Professor Jose Lado, Aalto University School of Science, Department of Applied Physics
Much like how water transitions between ice and liquid, systems of many quantum particles can also undergo phase transitions. In water, this change occurs when the temperature is altered, which is an external parameter. Similarly, in quantum systems, phase transitions can be triggered by varying different external parameters, such as the strength of a magnetic field. When these phase transitions happen at absolute zero temperature, they are referred to as quantum phase transitions. These transitions arise due to the collective behavior of many particles. For example, in the formation of ice, many water molecules organize into a regular lattice. In quantum spin systems, all the spins may align in the same direction, resulting in a ferromagnet — just like the magnets we encounter in everyday life. Quantum phase transitions are particularly difficult to study because understanding systems of many quantum particles involves working with matrices that grow exponentially with the number of particles.
In this thesis, we study phase transitions using a formalism inspired by the work of Lee and Yang, combined with state-of-the-art numerical techniques. Specifically, we investigate a function that encodes the behaviour of the system relative to a given phase. By determining where this function becomes zero in the complex plane, and observing how this location changes as the system size varies, we can pinpoint the locations of phase transitions. To achieve this, we simulate quantum many-body systems using numerical methods, which provide approximate solutions on computers. We employ two main techniques: First, we use tensor networks, which are collections of higher-dimensional generalizations of matrices. Second, we use neural network quantum states, which are mathematical functions originally developed for machine learning.
Using these numerical methods and the Lee-Yang formalism, we explore the phase diagrams of a simplified model for a ferromagnet, the transverse field Ising model, as well as the phase diagram of a model representing a chain of electron-like particles. Additionally, we apply our techniques to determine the phase diagram of a model for frustrated magnetism. This model features both antiferromagnetic phases and a so-called topological phase.
In summary, this thesis provides a fresh perspective on quantum phase transitions, combining the Lee-Yang formalism with advanced quantum many-body algorithms to better understand and identify these transitions.
Key words: Lee-Yang zeros, Matrix product states, Neural quantum states, Phase transitions
Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/
Contact information:
| pascal.vecsei@aalto.fi |
Doctoral theses at the School of Science: https://aaltodoc.aalto.fi/handle/123456789/52
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