Kavli Affiliate: Masahito Yamazaki
| First 5 Authors: Weiguang Cao, Masahito Yamazaki, Yunqin Zheng, ,
| Summary:
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.
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