We study boson–fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson–fermion duality between the Lieb–Liniger model and the Cheon–Shigehara model. We present an explicit construction of n-boson and n-fermion models which are dual to each other and characterized by n−1 distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson–fermion mapping, and the strong–weak duality. We also discuss a scale-invariant generalization of the boson–fermion duality.We study boson–fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson–fermion duality between the Lieb–Liniger model and the Cheon–Shigehara model. We present an explicit construction of n-boson and n-fermion models which are dual to each other and characterized by n−1 distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson–fermion mapping, and the strong–weak duality. We also discuss a scale-invariant generalization of the boson–fermion duality.

arXiv:2105.04288Annals of PhysicsOct 26, 202112 citations

BOSON-FERMION INTERACTIONS

V. A. Yatsun

Jan 1, 19920 citations

Fermions and Bosons

Philippe A. Martin, FRANÇOIS ROTHEN

Springer eBooksJan 1, 20020 citations

Boson-fermion duality with subsystem symmetry

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.