Quantum Phase Transition with a Simple Variational Ansatz
  We study the zero-temperature quantum phase transition between liquid and hcp solid helium-4. We use the variational method with a simple yet exchange-symmetric and fully explicit wavefunction. It is found that the optimized wavefunction undergoes spontaneous symmetry breaking and describes the quantum solidification of helium at 22 atm. The explicit form of the wavefunction allows to consider various contributions to the phase transition. We find that the employed wavefunction is an excellent candidate for describing both a first-order quantum phase transition and the ground state of a Bose solid. 
Y. Lutsyshyn, G. E. Astrakharchik, C. Cazorla, J. Boronat
cond-mat.quant-gas