Spin-based Hamiltonians

Spin-based Hamiltonians#

class HamHeisenberg(mu: ndarray, J_eq: ndarray, J_ax: ndarray, connectivity: ndarray | None = None)#

XXZ Heisenberg Hamiltonian.

__init__(mu: ndarray, J_eq: ndarray, J_ax: ndarray, connectivity: ndarray | None = None)#

Initialize XXZ Heisenberg Hamiltonian.

Parameters:

  • mu (np.ndarray) – Zeeman term

  • J_eq (np.ndarray) – J equatorial term

  • J_ax (np.ndarray) – J axial term

  • connectivity (np.ndarray) – symmetric numpy array that specifies the connectivity between sites

Notes

The form of the Hamiltonian is given by:

\[\hat{H}_{X X Z}=\sum_p\left(\mu_p^Z-J_{p p}^{\mathrm{eq}}\right) S_p^Z+\sum_{p q} J_{p q}^{\mathrm{ax}} S_p^Z S_q^Z+\sum_{p q} J_{p q}^{\mathrm{eq}} S_p^{+} S_q^{-}\]
generate_one_body_integral(dense: bool, basis='spinorbital basis')#

Generate one body integral.

Parameters:

  • dense (bool)

  • basis (str)

Return type:

scipy.sparse.csr_matrix or np.ndarray

generate_two_body_integral(sym=1, dense=False, basis='spinorbital basis')#

Generate two body integral in spatial or spinorbital basis.

Parameters:

  • basis (str) – [‘spinorbital basis’, ‘spatial basis’]

  • dense (bool) – dense or sparse matrix; default False

  • sym (int) – symmetry – [2, 4, 8] default is 1

Return type:

scipy.sparse.csr_matrix or np.ndarray

generate_zero_body_integral()#

Generate zero body term.

Returns:

zero_energy

Return type:

float

class HamIsing(mu: ndarray, J_ax: ndarray, connectivity: ndarray | None = None)#

Ising Hamiltonian.

__init__(mu: ndarray, J_ax: ndarray, connectivity: ndarray | None = None)#

Initialize XXZ Heisenberg Hamiltonian.

Parameters:

  • mu (np.ndarray) – Zeeman term

  • J_ax (np.ndarray) – J axial term

  • connectivity (np.ndarray) – symmetric numpy array that specifies the connectivity between sites

Notes

The form of the Hamiltonian is given by:

\[\hat{H}_{Ising}=\sum_p\mu_p^Z S_p^Z+\sum_{p q} J_{p q}^{\mathrm{ax}} S_p^Z S_q^Z\]
class HamRG(mu: ndarray, J_eq: ndarray, connectivity: ndarray | None = None)#

Richardson-Gaudin Hamiltonian.

__init__(mu: ndarray, J_eq: ndarray, connectivity: ndarray | None = None)#

Initialize XXZ Heisenberg Hamiltonian.

Parameters:

  • mu (np.ndarray) – Zeeman term

  • J_eq (np.ndarray) – J equatorial term

  • connectivity (np.ndarray)

Notes

The form of the Hamiltonian is given by:

\[\hat{H}_{RG}=\sum_p\left(\mu_p^Z-J_{p p}^{\mathrm{eq}}\right) S_p^Z+\sum_{p q} J_{p q}^{\mathrm{eq}} S_p^{+} S_q^{-}\]