HeisenbergModel#
- class HeisenbergModel(lattice, coupling_constants=(1.0, 1.0, 1.0), ext_magnetic_field=(0.0, 0.0, 0.0))[source]#
Bases:
LatticeModelThe Heisenberg model.
This class implements the following Hamiltonian:
\[H = - \vec{J} \sum_{\langle i, j \rangle} \vec{\sigma}_{i} \otimes \vec{\sigma}_{j} - \vec{h} \sum_{i} \vec{\sigma}_{i}\]where \(i,j\) refer to lattice nodes. The \(\sum_{\langle i, j \rangle}\) is performed over adjacent lattice nodes. This model assumes spin-\(\frac{1}{2}\) particles. Thus, \(\vec{\sigma}_{i} = (X_i, Y_i, Z_i)\) is a vector containing the Pauli matrices. \(\vec{J}\) is the coupling constant and \(\vec{h}\) is the external magnetic field, both with dimensions of energy.
This model is instantiated using a
Lattice. For example, using aLineLattice:line_lattice = LineLattice(num_nodes=10, boundary_condition=BoundaryCondition.OPEN) heisenberg_model = HeisenbergModel(line_lattice, (1.0, 1.0, 1.0), (0.0, 0.0, 1.0))
The transverse-field Ising model can be recovered as a special case of the Heisenberg model by limiting the model to spins that are parallel/antiparallel with respect to a transverse magnetic field:
heisenberg_model = HeisenbergModel(line_lattice, (0.0, 0.0, 1.0), (1.0, 0.0, 0.0))
- প্যারামিটার:
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
- interaction_matrix()#
Return the interaction matrix
- রিটার্নস:
The interaction matrix.
- রিটার্ন টাইপ:
- interpret(result)#
Interprets an
EigenstateResultin this hamiltonians context.- প্যারামিটার:
result (EigenstateResult) -- the result to add meaning to.