  Quantum phase transitions (QPTs) in qubit systems are known to produce
singularities in the entanglement, which could in turn be used to probe the
QPT. Current proposals to measure the entanglement are challenging however,
because of their nonlocal nature. Here we show that a double quantum dot
coupled locally to a spin chain provides an alternative and efficient probe of
QPTs. We propose an experiment to observe a QPT in a triple dot, based on the
well-known singlet projection technique.
