Fermionic Symmetry in Ichimatsu-Decomposed Lattice Models

TL;DR

This paper introduces lattice models with exact fermionic symmetries using an Ichimatsu pattern, enabling translation within the algebra of these symmetries, which is a novel structural approach.

Contribution

It proposes a new lattice model structure with fermionic symmetries linked to link variables, utilizing an Ichimatsu pattern to facilitate algebraic translation.

Findings

Exact fermionic symmetries relate fermions and link variables.

Ichimatsu pattern enables translation in the symmetry algebra.

New lattice model structure with unique symmetry properties.

Abstract

We present the lattice models with exact fermionic symmetries relating fermions and link variables. The plaquettes are distributed in an Ichimatsu pattern (chequered). We explain this peculiar structure allows us to have a translation in the algebra of the fermionic symmetries.