triqs.lattice.utils.TB_to_sympy(TBL, analytical=True, precision=6)[source]

returns the analytical form of the momentum space hamiltonian of the tight-binding model from a tight-binding lattice object by utilizing Fourier series

  • TBL (triqs TBLattice object) – triqs tight binding object

  • analytical (boolean, default = True) – whether to return the Hamiltonian in analytical (true) or numerical (false) form.

  • precision (integer, default = 6) – specifies the number of digits in the floating point amplitudes. The default value is 6 but the user can decrease it to help recognize similar hopping amplitudes, particularly for symmetrical hoppings across the crystal lattice


Hk – the Hamiltonian of the tight-binding model in momentum space. It can be output in either numerical form (Hk_numerical) or reduced analytical form (Hk) based on the user’s choice. The default output is the reduced analytical form. The numerical form depends solely on the k-space vector components while the analytical form takes into account both the k-space vector components and the lattice vectors

Return type:

NumPy array