Aspects of quantum entanglement in critical and topologically ordered systems

Entanglement;Critical systems;Topologically ordered systems

Wen, Xueda

关键词: Entanglement;    Critical systems;    Topologically ordered systems;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/98200/WEN-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Quantum entanglement plays an important role in characterizing the property of many-body systems and quantum field theories. In this thesis, we study the quantum entanglement in (1+1)-dimensional critical systems and (2+1)-dimensional topologically ordered phases. For (1+1)-d critical systems, we mainly study the non-equilibrium property of quantum entanglement, by focusing on three interesting cases: (i) the time evolution of entanglement hamiltonian during thermalization of a subsystem after a global quantum quench; (ii) time evolution of entanglement entropy after an inhomogeneous quantum quench; (iii) entanglement negativity evolution after a local quantum quench. For (2+1)-d topologically ordered phases, we use edge theory approach to study the topological entanglement entropy, mutual information and entnanglement negativity of Chern-Simons theories, which are further confirmed based on the surgey approach. In addition, we study the entanglement renormalization of topological insulators, and investigate the geometric and topological properties in the bulk of entanglement renormalization.