Efficient method to determine phase boundaries of quantum systems

The investigation of the phase behavior of substances has been a central subject in equilibrium thermodynamics due to the dramatic changes that take place in the macroscopic properties of substances during phase transitions [1]. Computer simulation has been an important tool to understand and predict the phase behavior of substances [2]. In most cases, computational studies can rely on classical simulations. However, when a substance undergoes a phase transition in a range of temperature and pressure in which the thermal energy is of the same order of that of the vibrational modes, quantum effects start playing a significant role in the phase behavior of the substance. In this work, we present an efficient method to determine phase diagrams of quantum systems through the dynamical integration of the Clausius-Clapeyron equation (d-CCI)[3]. The efficiency of the method stems from the fact that, starting from a single point at the coexistence boundary, one can calculate the entire coexistence curve using a single path integral Monte Carlo (PIMC) simulation [4], whereas in other methods many equilibrium simulations are required. In order to check the efficiency and reliability of the methodology, we applied it to the calculation of the solid-liquid coexistence boundary of neon in the range of low temperature, near the triple-point. Our results, which were obtained using a small fraction of the computer time usually employed in this kind of simulations, show a very good agreement with the experimental data [5].