Techniques for lower bounding spectral gaps in the quantum adiabatic algorithm
You might find the techniques here useful too:
http://arxiv.org/abs/1203.5801

A generalization of the above is on its way.

There are various references that give bounds for mixing times of Markov chains. Sometimes the gap of the quantum systems can be related to a the gap (largest to second largest) of a Markov chain, in which case the techniques such as rapidly mixing, high conductivity, gap upper bounds of Markov chains become relevant . Eg.
Persi Diaconis and Laurent Saloff-Coste, 'comparison theorems for reversible markov chains'

RM