Hubbard Hamiltonian
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According to this paper the per-site ground-state energy at half-filling can be written as a function of U:
However, the ground state for the two-site Hubbard model can be solved directly and the ground state for half filing band is written as
The problem
It turns out, that if I run the code to check the values obtained by these formulas are different.
So expression 1 is:
-1.04036865
Expression 2:
-1.561552812
Results obtained by calculating hamiltonian via my code and further solving with PyCI
-1.56155281
In addition to this, when I test results for a 3, 4 ... n site 1-d chain using hubbard model results should be in agreement with the expression 1, but they aren't :(
Overall it's clear that something is wrong with the interpretation of using expression 1. Even though the 2-site Hubbard model is tested already, I can't test it for the 1-d chain, because I'm not sure if there is a problem with a code or it's just not the right case for using expression 1
@PaulWAyers any ideas on how can I test it?
- Put 4 sites in a ring and try
- put 6 sites in the ring