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We study the transverse field Ising model on a kagome and a triangularlattice using high-order series expansions about the high-field limit. For thetriangular lattice our results confirm a second-order quantum phase transitionin the 3d XY universality class. Our findings for the kagome lattice indicate anotable instance of a disorder by disorder scenario in two dimensions. Thelatter follows from a combined analysis of the elementary gap in the high- andlow-field limit which is shown to stay finite for all fields h. Furthermore,the lowest one-particle dispersion for the kagome lattice is extremely flatacquiring a dispersion only from order eight in the 1/h limit. This behaviourcan be traced back to the existence of local modes and their breakdown which isunderstood intuitively via the linked cluster expansion.

Disorder by disorder and flat bands in the kagome transverse field Ising model