Mapping local Hamiltonians of fermions to local Hamiltonians of spins
F. Verstraete, J.I. Cirac
TL;DR
This paper presents a method to map local fermionic Hamiltonians onto local spin Hamiltonians in any dimension by extending the Jordan-Wigner transformation with auxiliary Majorana fermions, aiding numerical studies.
Contribution
It introduces a generalized mapping technique for fermions to spins in higher dimensions using auxiliary Majorana fermions, expanding beyond one-dimensional systems.
Findings
Mapping preserves locality in higher dimensions
Facilitates numerical simulations of fermionic systems
Extends Jordan-Wigner transformation to multiple dimensions
Abstract
We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan-Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.
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