Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Exact bosonization in two and three spatial dimensions and new classes of lattice gauge theory

Yu-An Chen, Anton Kapustin, Djordje Radicevic

Published Mar 5, 2019• 0 citations
OpenAlex

Related papers

Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

Yu-An Chen, Anton Kapustin, Đorđe Radičević

arXiv:1711.00515•Annals of Physics•Apr 11, 2018•94 citations

Ising lattice gauge theory in three dimensions

Paul Martin

Nuclear Physics B•Sep 1, 1983•9 citations

Jordan-Wigner Transformation in Higher Dimensions

1. Exact bosonization in two spatial dimensions and a new class of lattice gauge theories Authors: Yu-An Chen, Anton Kapustin, and Djordje Radicevic Annals of Physics 393, 234 (2018); DOI: 10.1016/j.aop.2018.03.024 arXiv:1711.00515 2. Constraints of kinematic bosonization in two and higher dimensions Authors: Arkadiusz Bochniak, Blazej Ruba, Jacek Wosiek, and Adam Wyrzykowski Phys. Rev. D […]

Journal Club for Condensed Matter Physics•Aug 31, 2021•1 citation

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

Chen, Yu-An

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.

•Jun 9, 2020•0 citations

Bosonization in two-dimensional field theory

Max A. Lohe, C. A. Hurst

•Jan 1, 1990•0 citations

Lattice versions of quantum field theory models in two dimensions

Anatoli G. Izergin, V. E. Korepin

Nuclear Physics B•Jun 1, 1982•189 citations
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.