1D tV model
1 Jordan Wigner transformation
Definition 1.1 (Jordan Wigner Transformation)
(1)
(1)
tV model can be viewed as an equivalent XXZ model.
Definition 1.2 (tV model)
(2)
(2)
1.1 Hopping term
(3)
(3)
1.2 Interaction term
(4)
(4)
perform summation
(5)
(5)
Definition 1.2.1 let
(6)
(6)
Thus the mapped system becomes
(7)
(7)
which is typically a XXZ model with magnetic field in z direction.