Models

This section contains the API documentation for the models module.

quantum1dIsing(kwargs)

Hamiltonian for the 1D transverse-field Ising model.

\[H = -J \left(\sum_{\langle ij \rangle} S_i^x S_j^x + h \sum_{i} S_i^z \right).\]
Keyword arguments

  • ‘J’ (double) – \(ZZ\) coupling, defaults to 1.

  • ‘h’ (double) – relative transverse field strength, defaults to 1.

  • ‘L’ (int) – system size, defaults to Inf.

  • ‘Symmetry’ (char) – symmetry group (‘Z1’, ‘Z2’ or ‘fZ2’), defaults to 'Z1'.

Returns

mpo (InfJMpo) – Ising Hamiltonian as a Jordan block MPO.

quantum1dHeisenberg(kwargs)

Hamiltonian for the 1D Heisenberg model.

\[H = J \sum_{\langle ij \rangle} \vec{S}_i \cdot \vec{S}_j + h \sum_{i} S_i^z\]
Keyword arguments

  • ‘Spin’ (double) – halfinteger or integer spin label, defaults to 1.

  • ‘J’ (double) – exchange coupling, defaults to 1.

  • ‘h’ (double) – magnetic field, defaults to 0.

  • ‘L’ (int) – system size, defaults to Inf.

  • ‘Symmetry’ (char) – symmetry group (‘U1’ or ‘SU2’), defaults to 'SU2'.

Returns

mpo (InfJMpo) – Heisenberg Hamiltonian as a Jordan block MPO.

quantum1dHubbard(u, mu, kwargs)

Hamiltonian for the 1D Hubbard model.

\[H = -\sum_{\langle ij \rangle} (c^+_i c_j + c^+_j c_i) + u \sum_i (1 - 2n_i^{\uparrow}) \cdot (1-2n_i^{\downarrow}) - \mu \sum_i (n_i^{\uparrow} + n_i^{\downarrow})\]
Arguments

  • u (double) – interaction strength.

  • mu (double) – chemical potential.

Keyword arguments

  • ‘Filling’ (double) – rational filling factor.

  • ‘Symmetry’ (char) – symmetry group, defaults to 'fZ2xSU2xU1'.

Returns

mpo (InfJMpo) – Hubbard Hamiltonian as a Jordan block MPO.

statmech2dIsing(kwargs)

MPO encoding the transfer matrix of the partition function of the 2D classical Ising model

\[\mathcal{Z} = \sum_{\{s\}} \prod_{\langle ij \rangle} \exp \left( \beta s_i s_j \right).\]
Keyword arguments

  • ‘beta’ (double) – inverse temperature.

  • ‘L’ (int) – system size, defaults to Inf.

  • ‘Symmetry’ (char) – symmetry group (‘Z1’, ‘Z2’), defaults to 'Z1'.

Returns

mpo (InfMpo or Finite) – MPO transfer matrix of the Ising partition function.