Spin 1/2 Operators -> Hubbard Operators
Assume
.
From the identities of spin operators,
,
where
and
are fermion operators described in
Fermion Operator -> Hubbard Operator
, the spin operators represented in Hubbard Operators are
.
Definition of Hubbard Operator
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. . 
, 
and 
are
fermion operators described in Fermion
Operator -> Hubbard Operator, the spin operators represented in
Hubbard Operators are 
.