07/17/2023
By Spasen Chaykov
The Kennedy College of Science, Department of Physics & Applied Physics, invites you to attend a Ph.D. Dissertation defense by Spasen Chaykov entitled "Entanglement entropy in discretized quantum field theory."
Degree: Doctoral
Date: Thursday, July 20, 2023
Time: 10 a.m.
Location: Hybrid, Olney 204; Via Zoom.
Committee Chair: Nishant Agarwal, Department of Physics & Applied Physics, University of Massachusetts Lowell
Committee Members:
- Archana Kamal, Department of Physics & Applied Physics, University of Massachusetts Lowell
- Viktor Podolskiy, Department of Physics & Applied Physics, University of Massachusetts Lowell
Abstract
In recent years, progress has been made on many of the long-standing questions in high-energy physics and quantum gravity utilizing concepts from information theory. One key object of study has been the von Neumann entropy, an important measure of the information in a given quantum system. In this thesis, we perform a systematic study of the entanglement entropy of discretized free scalar quantum field theories (QFTs). We first give a broad introduction to the topic of entanglement entropy in general, and specifically in QFT. We next define the theory that we study in the rest of the thesis by discretizing free scalar QFT in different dimensions. The resulting theory is equivalent to a system of linearly interacting quantum harmonic oscillators, and we study the entanglement entropy for such systems using both replica and covariance matrix methods. We then apply the formalism to a dynamical problem and demonstrate dynamical thermalization and Anderson localization following a global mass quench for systems without and with disorder. Lastly, we study an alternative discretization approach where the continuum wave functionals of QFT are mapped to oscillator wave functions, allowing for calculations that capture the continuum QFT entanglement entropy without the need to diagonalize a finite space Hamiltonian. We use this method to show that it can eliminate finite-size effects present in the dynamical calculation from the previous chapter and discuss how it can be generalized to different spacetimes.
In recent years, progress has been made on many of the long-standing questions in high-energy physics and quantum gravity utilizing concepts from information theory. One key object of study has been the von Neumann entropy, an important measure of the information in a given quantum system. In this thesis, we perform a systematic study of the entanglement entropy of discretized free scalar quantum field theories (QFTs). We first give a broad introduction to the topic of entanglement entropy in general, and specifically in QFT. We next define the theory that we study in the rest of the thesis by discretizing free scalar QFT in different dimensions. The resulting theory is equivalent to a system of linearly interacting quantum harmonic oscillators, and we study the entanglement entropy for such systems using both replica and covariance matrix methods. We then apply the formalism to a dynamical problem and demonstrate dynamical thermalization and Anderson localization following a global mass quench for systems without and with disorder. Lastly, we study an alternative discretization approach where the continuum wave functionals of QFT are mapped to oscillator wave functions, allowing for calculations that capture the continuum QFT entanglement entropy without the need to diagonalize a finite space Hamiltonian. We use this method to show that it can eliminate finite-size effects present in the dynamical calculation from the previous chapter and discuss how it can be generalized to different spacetimes.