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- W2177221036 abstract "To understand the new physics and richness ofquantum many-body system phenomena is one of the stimuli drivingthe condensed matter community forward. Importantly, the newinsights and solutions for condensed matter theory sometimes comefrom the developed and developing knowledge of high energy theory,mathematical and particle physics, which is also true the other wayaround: Condensed matter physics has been providing crucial hintsand playgrounds for the fundamental laws of high energy physics. Inthis thesis, we explore the aspects of symmetry, topology andanomalies in quantum matter with entanglement from both condensedmatter and high energy theory viewpoints. The focus of our researchis on the gapped many-body quantum systems includingsymmetry-protected topological states (SPTs) and topologicallyordered states (TOs). We first explore the ground state structuresof SPTs and TOs: the former can be symmetry twisted and the latterhas robust degeneracy. The Berry phases generated by transportingand overlapping ground state sectors potentially provide universaltopological invariants that fully characterize the SPTs and TOs.This framework provides us the aspects of symmetry and topology. Weestablish a field theory representation of SPT invariants in anydimension to uncover group cohomology classification and beyond – the former for SPTs with gapless boundary gauge anomalies, thelatter for SPTs with mixed gauge-gravity anomalies. We studytopological orders in 3+1 dimensions such as Dijkgraaf-Wittenmodels, which support multi-string braiding statistics; theresulting patterns may be analyzed by the mathematical theory ofknots and links. We explore the aspects of surface anomalies ofbulk gapped states from the bulk-edge correspondence: The gaugeanomalies of SPTs shed light on the construction of bosonicanomalies including Goldstone-Wilczek type, and also guide us todesign a non-perturbative lattice model regularizing the low-energychiral fermion/gauge theory towards the Standard Model whileovercoming the Nielsen-Ninomiya fermion-doubling problem withoutrelying on Ginsparg-Wilson fermions. We conclude by utilizingaspects of both quantum mechanical topology and spacetime topologyto derive new formulas analogous to Verlinde's viageometric-topology surgery. This provides new insights for higherdimensional topological states of matter." @default.
- W2177221036 created "2016-06-24" @default.
- W2177221036 creator A5079250808 @default.
- W2177221036 date "2015-01-01" @default.
- W2177221036 modified "2023-09-27" @default.
- W2177221036 title "Aspects of symmetry, topology and anomalies in quantum matter" @default.
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