# non-local correlated hopping term expressed as MPO

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For a Hubbard model with correlation hopping, the hopping term is

$$H_0=-J\sum_{<i,j>}a_i^{\dagger} F_0(\hat{n}_i-\hat{n}_j)a_j$$

with

$$F_0(\hat{n}_i-\hat{n}_j)=J_0(\Omega(\hat{n}_i-\hat{n}_j))$$

here, @@J_0@@ is first-order Bessel function. SInce @@F_0@@ is non-linear, it is impossible to express @@ F_0 @@ as a product of two local operators on sites i and j, i.e.

$$F_0(\hat{n}_i-\hat{n}_j) ?= O_i \cdot O_j$$

Then in this case, how can we perform DMRG as usual using ITensor ?

commented by (44.9k points)
Hi, do you have a question about this?
commented by (650 points)
yes, I have edited the question just now.
commented by (44.9k points)
Thanks,  but I don't have a good idea about this. What is Omega? What is F0? Could you provide a link to a reference since I haven't heard of correlation hopping before. Thanks -
commented by (650 points)
No problem, you may find details in this paper : PRL 109, 203005, eqn(4)