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We show how to map local fermionic problems onto local spin problems on alattice in any dimension. The main idea is to introduce auxiliary degrees offreedom, represented by Majorana fermions, which allow us to extend theJordan-Wigner transformation to dimensions higher than one. We also discuss theimplications of our results in the numerical investigation of fermionicsystems.Comment: Added explicit mappin

Mapping local Hamiltonians of fermions to local Hamiltonians of spins