000001145 001__ 1145 000001145 005__ 20240523045440.0 000001145 02470 $$a10.6082/M11Z4295$$2doi 000001145 037__ $$aTHESIS$$bDissertation 000001145 041__ $$aeng 000001145 245__ $$aBerry Phase Physics in Free and Interacting Fermionic Systems 000001145 260__ $$bUniversity of Chicago 000001145 269__ $$a2016 000001145 300__ $$a175 000001145 336__ $$aDissertation 000001145 502__ $$bPh.D. 000001145 542__ $$fUniversity of Chicago dissertations are covered by copyright. 000001145 590__ $$aBerry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting fermionic systems. We start with reviewing the semi-classical kinetic theory with Berry phase for a non-interacting ensemble of fermions -- a Berry Fermi gas -- which might be far-from-equilibrium. We particularly review the famous Berry phase contribution to the anomalous Hall current. We then provide a concrete and general path integral derivation for the semi-classical theory. Then we turn to the specific example of Weyl fermion, which exhibits the profound quantum phenomenon of chiral anomaly; we review how this quantum effect, and its closely related chiral magnetic effect and chiral vortical effect, arise from Berry phase in the semi-classical kinetic theory. We also discuss how Lorentz symmetry in the kinetic theory of Weyl fermion, seemly violated by the Berry phase term, is realized non-trivially; we provide a physical interpretation for this non-trivial realization, and discuss its mathematical foundation in Wigner translation. Next, we turn towards interacting fermionic systems. We consider Fermi liquid near equilibrium, and propose the Berry Fermi liquid theory -- the extension to Landau Fermi liquid theory incorporating Berry phase (and other) effects. In our proposed Berry Fermi liquid theory, we can show the Berry phase is a Fermi surface property, qualitatively unmodified by interactions. But there also arise new effects from interactions, most notably the emergent electric dipole moment which contributes to the anomalous Hall current in addition to the usual Berry phase contribution. We prove our proposed Berry Fermi liquid theory from quantum field theory to all orders in Feynman diagram expansion under very general assumptions. 000001145 653__ $$aanomalous Hall effect 000001145 653__ $$aBerry curvature 000001145 653__ $$aBerry phase 000001145 653__ $$aFermi liquid 000001145 653__ $$akinetic theory 000001145 653__ $$aWeyl fermion 000001145 690__ $$aPhysical Sciences Division 000001145 691__ $$aPhysics 000001145 7001_ $$aChen, Jingyuan$$uUniversity of Chicago 000001145 72012 $$aDam T. Son 000001145 8564_ $$9f18d7590-6c60-4424-9d6c-4c6b13616eb4$$ePublic$$s878832$$uhttps://knowledge.uchicago.edu/record/1145/files/Chen_uchicago_0330D_13349.pdf 000001145 902__ $$ahttp://hdl.handle.net/11417/91 000001145 903__ $$aMade available in DSpace on 2016-10-26T21:36:38Z (GMT). No. of bitstreams: 1 Chen_uchicago_0330D_13349.pdf: 878832 bytes, checksum: 88d83fd5da71ed96d8d2f2f9d5f82db9 (MD5) Previous issue date: 2016 000001145 909CO $$ooai:knowledge.uchicago.edu:1145$$pDissertations$$pGLOBAL_SET$$qthesis_test 000001145 945__ $$aUChicago Dissertations 000001145 945__ $$aPhysical Sciences Division - Dissertations 000001145 946__ $$aUChicago Dissertations 000001145 946__ $$aPhysical Sciences Division 000001145 980__ $$aMIG 000001145 983__ $$aDissertation