We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

arXiv:nucl-th/9408014Aug 15, 19940 citations

Boson-fermion duality with subsystem symmetry

Weiguang Cao, Masahito Yamazaki, Yunqin Zheng

arXiv:2206.02727Physical review. B./Physical review. BAug 29, 202223 citations

Physics Reports

Fermion to boson mappings revisited

Joseph N. Ginocchio, Calvin W. Johnson

Published Jan 1, 1996• 4 citations

Publisher

DOI: 10.1016/0370-1573(95)00035-6

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Weiguang Cao, Masahito Yamazaki, Yunqin Zheng

We explore an exact duality in $(2+1)$ dimensions $[(2+1)\mathrm{D}]$ 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 $(1+1)$ dimensions with a ${\mathbb{Z}}_{2}$ 0-form symmetry, presenting in a way generalizable to $(2+1)\mathrm{D}$ . We proceed to $(2+1)\mathrm{D}$ 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.We explore an exact duality in $(2+1)$ dimensions $[(2+1)\mathrm{D}]$ 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 $(1+1)$ dimensions with a ${\mathbb{Z}}_{2}$ 0-form symmetry, presenting in a way generalizable to $(2+1)\mathrm{D}$. We proceed to $(2+1)\mathrm{D}$ 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.

arXiv:2206.02727Physical review. B./Physical review. BAug 29, 202223 citations

We explore an exact duality in

(2+1)

dimensions

[(2+1)\mathrm{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)

dimensions with a

{\mathbb{Z}}_{2}

0-form symmetry, presenting in a way generalizable to

(2+1)\mathrm{D}

. We proceed to

(2+1)\mathrm{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.