Boson-fermion duality with subsystem symmetry

Article

关键词: QUANTUM;    BOSONIZATION;    DIMENSIONS;   

DOI  :  10.1103/PhysRevB.106.075150

来源: SCIE

【 摘 要 】

We explore an exact duality in (2 + 1) dimensions [(2 + 1)D] between the fermionization of a bosonic theory with a Z(2) subsystem symmetry and a fermionic theory with a 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 Z(2) 0-form symmetry, presenting in a way generalizable to (2 + 1)D. We proceed to (2 + 1)D with a 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.

【 授权许可】

Free