Geometry and topological phase of matter

Topological;Geometry

You, Yizhi

关键词: Topological;    Geometry;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/98214/YOU-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 】

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 thebilayer Half-filled Landau Level system where the two composite Fermi surfaceacquires interlayer coherence and forms bonding/anti-bonding composite fermisea. The corresponding interlayer coherent composite Fermi liquid(ICCFL) phaseprovides a straightforward landscape to verify the Dirac nature in Son's theoryand extract the hidden Berry phase structure of the composite Fermi surface.The ICCFL phase contains two Fermi surfaces which are detached in most regionsbut 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 withdeconfined $\frac{\pi}{2}$ gauge flux and the phase transition toward ICCFLcontains a Lifshitz criticality with $z=3$ dynamical exponent. In addition, theexciton order parameter carries topological spin number so the ICCFL contains aunique Wen-Zee term which connects EM response with the background geometrycurvature.