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Instantons in Parton Gauge Theories of Condensed Matter
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- Author / Creator
- Ganesh, Sankaranarayanan
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This thesis broadly investigates monopole-driven confinement transitions in parton gauge theories of fractionalized phases of matter. The first chapter studies the Dirac spin liquid, a 2d fractionalized Mott insulator with gapless Dirac fermion excitations coupled to a compact U(1) gauge field. We use semiclassical instanton methods not relying on conformal symmetry to construct all monopole operators as ’t Hooft vertices – instanton-induced interactions between fermions that have their origin in zero modes of the Euclidean Dirac operator in an instanton background. These monopole operators serve as order parameters for conventionally ordered states proximate to the Dirac spin liquid, as determined by their quantum numbers under lattice symmetries, which we are able to capture on bipartite lattices. Chapter 2 is a detailed technical description of instanton-induced interactions and their symmetry-breaking effects in CQED3, motivated by a fermionic parton description of hardcore bosons on a 2d lattice with U(1) symmetry. We show how the proliferation of instantons carrying fermion zero modes can lead to spontaneous breakdown of this symmetry, leading to either a conventional superfluid or an exotic ‘paired superfluid’. The last chapter generalizes this study to Ising spins on a 2d lattice with Z2 symmetry, represented by N Majorana partons. By varying the Chern number of the Majorana bandstructure, we access chiral spin liquid, paramagnetic, and long-range ordered phases of the Ising spins. A certain SO(N) Chern-Simons gauge theory with massless Majorana fermions is argued to be the critical theory that interpolates between these different phases. Finally, Z2-charged monopoles are shown to drive confinement in such a theory, leading to a magnetic phase with spontaneous breakdown of the Ising Z2 symmetry.
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- Graduation date
- Fall 2024
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.