Short-Range Entangled Phases of Fermions
This thesis is an attempt to understand the physics of short-range entangled phases of fermions through several related approaches. The first angle is topological quantum field theory. We discuss the classification of interacting fermionic short-range entangled phases by spin cobordism and give an a...
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| Format: | Others |
| Language: | en |
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2019
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| Online Access: | https://thesis.library.caltech.edu/11588/1/Turzillo-THESIS-final.pdf Turzillo, Alexander Michael (2019) Short-Range Entangled Phases of Fermions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3JR4-8G12. https://resolver.caltech.edu/CaltechTHESIS:05312019-162611521 <https://resolver.caltech.edu/CaltechTHESIS:05312019-162611521> |
| Summary: | This thesis is an attempt to understand the physics of short-range entangled phases of fermions through several related approaches. The first angle is topological quantum field theory. We discuss the classification of interacting fermionic short-range entangled phases by spin cobordism and give an algebraic characterization of unoriented equivariant bosonic topological quantum field theories in one spatial dimension. A second tool is tensor network representation. We develop the formalism of fermionic matrix product states and use it to derive the stacking group law for one dimensional symmetry-enriched fermionic short-range entangled phases. We also study its relationship with state sum constructions of topological quantum field theories and develop a state sum construction for pin-minus theories in one spatial dimension. The third approach is topological band theory. We classify free fermionic phases enriched by a unitary symmetry in any dimension and determine the map into the interacting classification. |
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