Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions

Understand

We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest.

• The correspondence between fermionic and bosonic operators is established with the help of auxiliary Majorana fermions.
• The current construction is applicable to general lattices with even coordination number and an arbitrary number of fermion flavors.
• The approach is demonstrated on the single-orbital square, triangular and cubic lattices for spin-1/2 fermions.