Hello Rabiu,
of course, the answer to your question depends on what you actually intend to investigate -- especially, whether the molecules are bosonic or fermionic.
If they are bosons, I can recommend to you a method which goes beyond the Bose-Hubbard Hamiltonian: the multiconfigurational time-dependent Hartree for bosons, or in short MCTDHB (see http://MCTDHB.org and http://link.aps.org/doi/10.1103/PhysRevA.77.033613 ). MCTDHB is a variational method, where the field operator is expanded in a time-dependent basis -- as opposed to Wannier functions in the case of the Bose-Hubbard Hamiltonian. The time-dependent basis allows for optimally covering a larger fraction of N-particle Hilbert space. Recently, it was shown that the method can provide numerically exact solutions of the full many-body problem (see http://link.aps.org/doi/10.1103/PhysRevA.86.063606 ).
In the case of fermions, there exists the multiconfigurational time-dependent Hartree method for fermions (MCTDHF, seehttp://publish.aps.org/search?c[][operator]=AND&c[][field]=author&c[][value]=&c[][operator]=AND&c[][field]=abstitle&c[][value]=MCTDHF&c[][operator]=AND&c[][field]=fulltext&c[][value]=&sort=recent&per_page=25&start_date=&end_date= ). It relies on the same idea, i.e., to expand the field operator in a time-dependent basis set. Of course, the many-body basis is slater determinants and not permanents in this case.
Hope that this gets you a step further.
Regards,
Axel
Thank you Axel, Your answer was really helpful! In fact my question is about my PhD work. I am actually concerned with how to emulate High-Tc superconducting mechanism, Quantum magnetism, and possibly Thermodynamic properties as well as transport properties. Hubbard model can provide only approximate answers to some of these universal phenomenon
Hello Rabiu,
For large particle numbers it is difficult to get more than an approximate description, especially in the case of strong interparticle interactions.
But it might be very helpful for you to first try and understand the few-particle quantum dynamics (maybe by using one of the above methods?). By generalization of the conjectures found for a few particles (molecules, electrons, bosons, etc.) you might find and explain the properties of the larger systems (quantum magnetism, transport properties, etc.).
At least in my case (tunneling dynamics in many-boson systems), this approach led to some valuable insight (see http://www.pnas.org/content/early/2012/07/31/1201345109.abstract ).
Good luck!
Regards,
Axel
Thank you Axel, I really appreciate that. I am very fine with Hubbard model. But MCTDHF(B) is not very familar, eventhough I have learnt Hatree-Fock Space/Theory in Solid State Physics some few years ago.
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