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We present an accurate ab initio tight-binding model, capable of describingthe dynamics of Dirac points in tunable honeycomb optical lattices following arecent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)].Our scheme is based on first-principle maximally localized Wannier functionsfor composite bands. The tunneling coefficients are calculated for differentlattice configurations, and the spectrum properties are well reproduced withhigh accuracy. In particular, we show which tight binding description is neededin order to accurately reproduce the position of Dirac points and thedispersion law close to their merging, for different laser intensities.

Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices