Fermi Hubbard Model on square lattice

Ground state energy

The following codes could compute the ground state energy of the Fermi Hubbard model on square lattice.

using QuantumLattices
using ExactDiagonalization
using LinearAlgebra: eigen

# define the unitcell of the square lattice
unitcell = Lattice([0.0, 0.0]; name=:Square, vectors=[[1.0, 0.0], [0.0, 1.0]])

# define a finite 3×4 cluster of the square lattice with open boundary condition
lattice = Lattice(unitcell, (3, 4))

# define the Hilbert space (single-orbital spin-1/2 complex fermion)
hilbert = Hilbert(site=>Fock{:f}(1, 2) for site=1:length(lattice))

# define the quantum number of the sub-Hilbert space in which the computation to be carried out
# here the particle number is set to be `length(lattice)` and Sz is set to be 0
quantumnumber = SpinfulParticle(length(lattice), 0)

# define the terms, i.e. the nearest-neighbor hopping and the Hubbard interaction
t = Hopping(:t, -1.0, 1)
U = Hubbard(:U, 8.0)

# define the exact diagonalization algorithm for the Fermi Hubbard model
ed = ED(lattice, hilbert, (t, U), quantumnumber)

# find the ground state and its energy
eigensystem = eigen(matrix(ed); nev=1)

# Ground state energy should be -4.913259209075605
print(eigensystem.values)
[-4.913259209075602]