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2017-05-19 Fradkin, Eduardo Hughes, Taylor Cooper, Lance Peng, Jen-Chieh You, Yizhi 2017-09-29T16:39:01Z 2017-09-29T16:39:01Z 2019-09-30T09:15:14Z 2017-08 In this thesis, I will first derive and study the effective field theories of isotropic-nematic quantum phase transitions of Quantum states. The low-energy theory of the nematic field has z=2 dynamics due to a Berry phase of the order parameter, which is related to the Hall viscosity in parity and time-reversal-symmetry (TRS) broken states. The vortex of the nematic field, which is physically a disclination, creates a nonzero geometry curvature in the disclination core. The leading coupling between the nematic field and gauge field includes a Wen-Zee term which links the geometry curvature with the gauge theory. In the second part of this thesis, I investigate the geometry related issues in Weyl semimetals and SPT states, and explore the novel character of geometry defect in SPT states inherited from the topological nature of manybody system. In addition, I would introduce a general way to induce topological phase transition via decorated defect condensate. In the final part of this thesis, I begin with the bilayer Half-filled Landau Level system where the two composite Fermi surface acquires interlayer coherence and forms bonding/anti-bonding composite fermi sea. The corresponding interlayer coherent composite Fermi liquid(ICCFL) phase provides a straightforward landscape to verify the Dirac nature in Son's theory and extract the hidden Berry phase structure of the composite Fermi surface. The ICCFL phase contains two Fermi surfaces which are detached in most regions but adhesive at two hot spots. Such nematic structure is a consequence of the Berry phase encoded in the Dirac Fermi surface which is absent in HLR theory. Due to the nematicity in ICCFL, the system supports half-quantum vortex with deconfined $\frac{\pi}{2}$ gauge flux and the phase transition toward ICCFL contains a Lifshitz criticality with $z=3$ dynamical exponent. In addition, the exciton order parameter carries topological spin number so the ICCFL contains a unique Wen-Zee term which connects EM response with the background geometry curvature. Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01 The student, Yizhi You, accepted the attached license on 2017-05-17 at 22:20. The student, Yizhi You, submitted this Dissertation for approval on 2017-05-17 at 22:23. This Dissertation was approved for publication on 2017-05-19 at 13:37. DSpace SAF Submission Ingestion Package generated from Vireo submission #11162 on 2017-09-29 at 11:13:07 Made available in DSpace on 2017-09-29T16:39:01Z (GMT). No. of bitstreams: 2 YOU-DISSERTATION-2017.pdf: 2317273 bytes, checksum: 295227b290f01ffe107897d66e9345a4 (MD5) LICENSE.txt: 4206 bytes, checksum: caf2eb0714a6f9e5ea8ae1e6401e7a88 (MD5) Previous issue date: 2017-05-19 Embargo set by: Colleen Fallaw for item 103361 Lift date: 2019-09-29T16:39:52Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Embargo set by: Colleen Fallaw for item 103361 Lift date: 2019-09-29T17:52:45Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Limited Restriction Lifted for Item 103361 on 2019-09-30T09:15:14Z. application/pdf http://hdl.handle.net/2142/98214 en Copyright 2017 Yizhi You Topological Geometry Geometry and topological phase of matter text text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.