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Abstract
We show that the physical system consisting of trapped ions interacting with lasers
may undergo a rich variety of quantum phase transitions. By changing the laser intensities
and polarizations the dynamics of the internal states of the ions can be controlled,
in such a way that an Ising or Heisenberg-like interaction is induced between effective
spins. Our scheme allows us to build an analogue quantum simulator of spin systems
with trapped ions, and observe and analyze quantum phase transitions with unprecedent
opportunities for the measurement and manipulation of spins.