Antiferromagnetic Heisenberg Model on square lattice

Ground state energy

The following codes could compute the ground state energy of the antiferromagnetic Heisenberg 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 4×4 cluster of the square lattice with open boundary condition
lattice = Lattice(unitcell, (4, 4))

# define the Hilbert space (spin-1/2)
hilbert = Hilbert(Spin{1//2}(), length(lattice))

# define the quantum number of the sub-Hilbert space in which the computation to be carried out
# for the ground state, Sz=0
quantumnumber = Sz(0)

# define the antiferromagnetic Heisenberg term on the nearest neighbor
J = Heisenberg(:J, 1.0, 1)

# define the exact diagonalization algorithm for the antiferromagnetic Heisenberg model
ed = ED(lattice, hilbert, J, quantumnumber)

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

# Ground state energy should be -9.189207065192935
print(eigensystem.values)

[-9.189207065192967]