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Exact Bosonization in All Dimensions: the Duality Between Fermionic and Bosonic Phases of Matter

Citation

Chen, Yu-An (2020) Exact Bosonization in All Dimensions: the Duality Between Fermionic and Bosonic Phases of Matter. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/593v-5r52. https://resolver.caltech.edu/CaltechTHESIS:06082020-083409184

Abstract

We describe an n-dimensional (n≥2) analog of the Jordan-Wigner transformation, which maps an arbitrary fermionic system to Pauli matrices while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization gives a duality between any fermionic system in arbitrary n spatial dimensions and a new class of (n-1)-form Z₂ gauge theories in n dimensions with a modified Gauss’s law. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model, and 3d bosonization, including a solvable Z₂ lattice gauge theory with Dirac cones in the spectrum. This bosonization formalism has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the manifold, a key feature for defining fermions. A new formula for Stiefel-Whitney homology classes on lattices is derived. We also derive the Euclidean actions for the corresponding lattice gauge theories from the bosonization. The topological actions contain Chern-Simons terms for (2+1)D or Steenrod Square terms for general dimensions. Finally, we apply the bosonization to construct various bosonic or fermionic symmetry-protectedtopological (SPT) phases. It has been shown that supercohomology fermionic SPT phases are dual to bosonic higher-group SPT phases.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:bosonization; symmetry protected topological phases
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Thesis Committee:
  • Chen, Xie (chair)
  • Kapustin, Anton N.
  • Alicea, Jason F.
  • Motrunich, Olexei I.
Defense Date:25 May 2020
Funders:
Funding AgencyGrant Number
US Department of Energy, Office of Science, Office of High Energy PhysicsDE-SC0011632
Record Number:CaltechTHESIS:06082020-083409184
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:06082020-083409184
DOI:10.7907/593v-5r52
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aop. 2018.03.024DOIArticle adapted for ch. 2
https://doi.org/10.1103/PhysRevB.100.245127DOIArticle adapted for ch. 3
https://arxiv.org/abs/1911.00017arXivArticle adapted for ch. 4
ORCID:
AuthorORCID
Chen, Yu-An0000-0002-8810-9355
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13788
Collection:CaltechTHESIS
Deposited By: Yu An Chen
Deposited On:09 Jun 2020 19:34
Last Modified:16 Jun 2020 21:15

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