FermiHubbardModel

class FermiHubbardModel(lattice, onsite_interaction)

Bases: LatticeModel

The Fermi-Hubbard model.

This class implements the following Hamiltonian:

\[H = \sum_{i, j}\sum_{\sigma = \uparrow, \downarrow} t_{i, j} c_{i, \sigma}^\dagger c_{j, \sigma} + U \sum_{i} n_{i, \uparrow} n_{i, \downarrow},\]

where \(c_{i, \sigma}^\dagger\) and \(c_{i, \sigma}\) are creation and annihilation operators of a fermion at the site \(i\) with spin \(\sigma\). The operator \(n_{i, \sigma}\) is the number operator, which is defined by \(n_{i, \sigma} = c_{i, \sigma}^\dagger c_{i, \sigma}\). The matrix \(t_{i, j}\) is a Hermitian matrix called the interaction matrix. The parameter \(U\) represents the strength of the on-site interaction.

This model is instantiated using a Lattice. For example, using a LineLattice:

line_lattice = LineLattice(num_nodes=10, boundary_condition=BoundaryCondition.OPEN)

fermi_hubbard_model = FermiHubbardModel(
    line_lattice.uniform_parameters(
        uniform_interaction=-1.0,
        uniform_onsite_potential=0.0,
    ),
    onsite_interaction=5.0,
)

প্যারামিটার:

• lattice (Lattice) -- Lattice on which the model is defined.

• onsite_interaction (complex) -- The strength of the on-site interaction.

Attributes

lattice

Return the input lattice.

Note, that this returns the internal lattice object without copying it. Thus, changing the returned lattice object, will affect the internal lattice stored in this Hamiltonian.

register_length

Methods

hopping_matrix()

Return the hopping matrix.

রিটার্ন টাইপ:

ndarray

interaction_matrix()

Return the interaction matrix

রিটার্নস:

The interaction matrix.

রিটার্ন টাইপ:

ndarray

interpret(result)

Interprets an EigenstateResult in this hamiltonians context.

প্যারামিটার:

result (EigenstateResult) -- the result to add meaning to.

second_q_op()

Return the Hamiltonian of the Fermi-Hubbard model in terms of FermionicOp.

রিটার্নস:

The Hamiltonian of the Fermi-Hubbard model.

রিটার্ন টাইপ:

FermionicOp