FermiHubbard1D

class FermiHubbard1D(num_sites, particles_up, particles_down, hop_strength, int_strength, potential)

Describes a one-dimensional Fermi-Hubbard model with open boundary conditions.

Initialize a one-dimensional fermi-hubbard system. In second quantization this system is described by the Hamiltonian

\(H = \sum_{i=1,\sigma}^{L-1} - J_i (f^\dagger_{i,\sigma} f_{i+1,\sigma} + f^\dagger_{i+1,\sigma} f_{i,\sigma}) + U \sum_{i=1}^{L} n_{i,\uparrow} n_{i,\downarrow} + \sum_{i=1,\sigma}^{L} \mu_i n_{i,\sigma}\)

Parameters:

• num_sites (int) – number of lattice sites in the 1D chain.

• particles_up (int) – total number of spin-up particles in the lattice

• particles_down (int) – total number of spin-down particles in the lattice

• hop_strength (float) – strength of hopping between sites

• int_strength (float) – strength of the local interaction

• potential (List[float]) – list of local phases, must be on length num_wires

Raises:

QiskitColdAtomError – if the length of the potential does not match the system size.

Attributes

FermiHubbard1D.size

Return the number of sites of the problem.

Methods

FermiHubbard1D.to_circuit([time])	Wrap the generator of the system in a QuantumCircuit.
FermiHubbard1D.to_fermionic_op()	Construct the hamiltonian of the lattice as a FermionicOp.