# LatticeWannier

This page gives hints on how to build and run lattice Wannier function (LWF’s) models, including: * How to build LWF’s from phonon calculations.

## Introduction¶

The lattice Wannier functions (LWF’s) are localized functions of atomic displacements in crystal structures which are the analogue of electronic Wannier functions. They could be used as basis set of effective Hamiltonians for the description of lattice distortions.

In anaddb, we can use the “selected cloumns of the density matrix” (SCDM-k) algorithm for the construction of the LWF’s, and the Hamiltonian of them within the harmonic approximation. Starting from that, we can build structures with various amplitudes of LWF’s and compute the energies of them. Then the anharmonic interaction between the LWF’s can be parameterized and added to the Hamiltonian. We can then run dynamics for the LWF’s with the Hamiltonian. Since the LWF’s can be constructed to give good description for a few phonon branches relevant to the phenomenons under study with the number of degrees of freedom largely reduced, it allows for simplification of the model without dropping the essential physics. The difficulty to fit of the anharmonic interaction, which grows with the number of degrees of freedoms, is thus much more easier. It also reduces the requirement for computational power when doing the dynamics.

## Tutorials¶

[[tutorial:lattice_wannier][How to build Lattice Wannier functions]] : The tutorial on how to build LWF’s with anaddb from phonon calculations.

basic:

• lwf_anchor_ibands Lattice Wannier Function: the ANCHOR Indices of BANDS
• lwf_anchor_proj Lattice Wannier Function ANCHOR point PROJection
• lwf_anchor_qpt Lattice Wannier Function: the ANCHOR QPoinTs
• lwf_disentangle Lattice Wannier Function DISENTANGLE function
• lwf_mu Lattice Wannier Function: the MU value
• lwf_ngqpt Lattice Wannier Function: the Number of Grid of Q-PoinTs
• lwf_nwann Lattice Wannier Function: Number of WANNier functions
• lwf_projector Lattice Wannier Function: the PROJECTORs
• lwf_sigma Lattice Wannier Function: the sigma value
• lwfflag Lattice Wannier Function Flag

tutorial:

v9: