Boson-fermion duality with subsystem symmetry

Abstract

We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a ${\mathbb{Z}}_2$ subsystem symmetry and a fermionic theory with a ${\mathbb{Z}}_2$ subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. We first revisit the standard boson-fermion duality in $(1+1)$d with a ${\mathbb{Z}}_2$ 0-from symmetry, presenting in a way generalizable to $(2+1)$d. We proceed to $(2+1)$d with a ${\mathbb{Z}}_2$ subsystem symmetry and establish the exact duality on the lattice by using the generalized Jordan-Wigner map, with a careful discussion on the mapping of the twist and symmetry sectors. This motivates us to introduce the subsystem Arf invariant, which exhibits a foliation structure.

39 pages, 4 figures; a few references and minor corrections added, published in PHYSICAL REVIEW B

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Cited by in corpus (13)

• Non-Invertible Duality Transformation Between SPT and SSB Phases
• Subsystem Non-Invertible Symmetry Operators and Defects
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Foliated BF theories and Multipole symmetries
• Generating Lattice Non-invertible Symmetries
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Error-correcting codes for fermionic quantum simulation
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• The exact susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions