Ab initio derivation of Hubbard models for cold atoms in optical lattices

TL;DR

This paper presents an ab initio method to derive accurate Hubbard models for various optical lattice potentials, including honeycomb and Kagomé lattices, using maximally-localized Wannier functions and a robust initialization procedure.

Contribution

The authors develop a new ab initio approach to derive Hubbard models for optical lattices, including a robust Wannier basis initialization and validation against original band structures.

Findings

Accurate Hubbard models derived for honeycomb and Kagomé lattices.

Validated models by comparing interpolated band structures.

Provided open-source MATLAB code for the procedure.

Abstract

We derive ab initio local Hubbard models for several optical lattice potentials of current interest, including the honeycomb and Kagom\'{e} lattices, verifying their accuracy on each occasion by comparing the interpolated band structures against the originals. To achieve this, we calculate the maximally-localized generalized Wannier basis by implementing the steepest-descent algorithm of Marzari and Vanderbilt [N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)] directly in one and two dimensions. To avoid local minima we develop an initialization procedure that is both robust and requires no prior knowledge of the optimal Wannier basis. The MATLAB code that implements our full procedure is freely available online at http://ccpforge.cse.rl.ac.uk/gf/project/mlgws/.