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Wen, Xueda 2017-09-29T17:45:11Z Ryu, Shinsei Hughes, Taylor Eckstein, James DeMarco, Brian 2017-09-29T17:45:11Z 2020-03-03T10:15:39Z 2017-07-06 2017-08 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. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2019-08-01 The student, Xueda Wen, accepted the attached license on 2017-07-06 at 09:15. The student, Xueda Wen, submitted this Dissertation for approval on 2017-07-06 at 09:26. This Dissertation was approved for publication on 2017-07-06 at 16:51. DSpace SAF Submission Ingestion Package generated from Vireo submission #11323 on 2017-09-29 at 10:46:45 Made available in DSpace on 2017-09-29T17:45:11Z (GMT). No. of bitstreams: 2 WEN-DISSERTATION-2017.pdf: 5037080 bytes, checksum: fe2685b7147f09a2b7128e9a0e8ffe3f (MD5) LICENSE.txt: 4206 bytes, checksum: 9714397c87d4bb64962d51deb912518d (MD5) Previous issue date: 2017-07-06 Embargo set by: Colleen Fallaw for item 103441 Lift date: 2019-09-29T17:48:06Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103441 Lift date: 2020-03-02T19:56:41Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103441 Lift date: 2020-03-02T19:59:52Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103441 Lift date: 2020-03-02T20:02:46Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 103441 on 2020-03-03T10:15:39Z. application/pdf http://hdl.handle.net/2142/98200 en Copyright 2017 Xueda Wen Entanglement Critical systems Topologically ordered systems Aspects of quantum entanglement in critical and topologically ordered systems text text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.