Bachelor Thesis: Entanglement Entropy in Two-dimensional Conformal Field Theory Supervision: dr Artur Pietrykowski
My thesis is a good chunk of theoretical physics requiring some mathematical knowledge. From perspective of programming, it coinatins code written in Mathematica for XX Model - Appendix A.
Technologies used:
- Mathematica
- LaTeX
The study has three major purposes: to define the Quantum Mechanics and the 2-dimensional Conformal Field Theory, to derive the entanglement entropy for a given set of systems in the frame of the 2-dimensional Conformal Field Theory and show its application to 1-dimensional statistical systems considering an example of quantum XX model.
In the first chapter of the work there is given a background of historical and current researches treating the entanglement. In the second chapter there is given an introduction to the Quantum Mechanics with an emphasis on quantum entanglement, next the picture is generalised to the Quantum Field Theory formalism. The third chapter defines the Conformal Field Theory with a special considerations of a 2-dimensional case is defined. The fourth chapter shows methods of deriving the entanglement entropy in the frame of 2-dimensional Conformal Field Theory for three cases: an interval at zero temperature, an interval at nonzero temperature and an interval on a circle at zero temperature. In the fifth chapter there is considered the quantum 1-dimensional XX model as an example of 1-dimensional statistical systems. Its ground state is derived what enables one to calculate the entanglement entropy in such a system and show that at its critical point it agrees with the theoretical prediction.
The thesis shows entanglement entropy in a perspective of the 2-dimensional Conformal Field Theory and that is applicable to 1-dimensional statistical models at their critical point.