Bose-Einstein Condensation and the Lambda Transition for Interacting Lennard-Jones Helium-4

An introduction to Bose-Einstein condensation and the $\lambda$-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.