Phase boundary between the fractional quantum Hall liquid and the Wigner crystal at low filling factors and low temperatures: A path integral Monte Carlo study

摘要

We generalize a path integral Monte Carlo formula to investigate the phase boundary between the fractional quantum Hall liquid and the Wigner crystal for a two-dimensional electron (fermion) system in the presence of strong magnetic fields and at low temperatures. At very low temperature, the state of the system is found to be a solid at filling factors ν=1/7, 1/9, and 1/11, while the state remains liquidlike at ν=1/3 and 1/5. The temperature-density phase diagrams are obtained at low filling factors. At ν=1/7 and a fixed electron density, the calculated melting temperature is ～220 mK, in good agreement with some experimental results. The nature of the phase transition is suggested to be continuous.