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ghb24 / NECI_STABLE

Standalone NECI codebase designed for FCIQMC and other stochastic quantum chemistry methods.
GNU General Public License v3.0
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How to define a periodic hubbard lattice using FCIDUMP? #17

Open simonganne01 opened 2 months ago

simonganne01 commented 2 months ago

Hello,

I was looking through the examples and I saw an example of a periodic hubbard model in an FCIDUMP file, several actually. But I dont undarstant how it is constructed and how the program knows the periodic extensions. Can anyone explain to me how this works or point me to some more documentation regarding this? Thank in advance

MaruSongMaru commented 2 months ago

Hello,

the idea is to view a Hubbard Hamiltonian as a special limit of a general abinitio Hamiltonian, where there are only certain types of integrals: uniform one-body integrals for neighboring sites and on-site Coulomb integrals $$(ii|ii)$$. These two types correspond to the $$t$$ and $$U$$ parameters, respectively. The relationships can be shown by comparing the Hamiltonians.

Therefore, performing a calculation using an artificial FCIDUMP file containing only those integrals is equivalent to solving the Hubbard Hamiltonian. This also means you can recover the lattice information from the FCIDUMP, particularly, one-body integrals. An artificial FCIDUMP file of a periodic system has to have one-body integrals connecting end sites to wrap the boundaries.

NECI also has excitation generators for lattice models. This does not require reading in an FCIDUMP file. You can find some examples, for example https://github.com/ghb24/NECI_STABLE/blob/master/test_suite/neci/tc/real-space-hub-hopping-tc-1x6/neci.inp.