Testing Problems

[RichRick1]

So far there are implemented (not int the best way):

1. PPP Hamiltonian (superclass)
2. Hubbard Hamiltonian (child class)
3. Huckel Hamiltonian (child class)

The main method is get_hamilton which returns zero, one and two body integrals as Numpy arrays.

Problems appears when testing an existing code. So far, there are couple of tests.

1. lTwo site Hubbard model which works great and available as test_1
2. According to this paper the per-site ground-state energy at half-filling can be written as a function of U:
   
   The values of this expression is -1.04036865, however proposed code doesn't return this answer.
   A good idea is test the same half-filling band but with more sites.

All code is available here: https://github.com/theochem/ModelHamiltonian/blob/upd/upd/Huckel_Hamiltonian.py

[PaulWAyers]

Gerald Knizia has a code for Hubbard models.
http://www.iboview.org/bin/bethe_ansatz.20140603.tar.bz2

This program can calculate a number of (exact) ground state properties of the infinite 1D Hubbard model, at arbitrary fillings (n) and couplings strengths (U), using the Bethe Ansatz solution.
Supported are energies/site, chemical potentials, metal-insulator transitions (1-particle gaps), and on-site spin correlation functions/particle number correlation functions.

Background: The 1D Hubbard model is one of the few exactly solvable model systems for strong correlation; this program computes reference data against which new electronic structure programs can be compared.

This is from Gerald's website.
https://sites.psu.edu/knizia/software/

[PaulWAyers]

The Pariser-Parr-Pople parameters are given explicitly for benzene here.
https://www.sciencedirect.com/science/article/pii/0009261488803749?via%3Dihub
See below equation 8.

[PaulWAyers]

A few other possibly useful references. This one has explicit formulations of the occupations numbers
https://aip.scitation.org/doi/10.1063/1.1425408

and this is also maybe useful
https://journals.aps.org/prb/pdf/10.1103/PhysRevB.30.4267
https://hrcak.srce.hr/file/166534
https://arxiv.org/pdf/physics/0207086.pdf