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

Abstract

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 $\ensuremath{\nu}=1∕7$, $1∕9$, and $1∕11$, while the state remains liquidlike at $\ensuremath{\nu}=1∕3$ and $1∕5$. The temperature-density phase diagrams are obtained at low filling factors. At $\ensuremath{\nu}=1∕7$ and a fixed electron density, the calculated melting temperature is $\ensuremath{\sim}220\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$, in good agreement with some experimental results. The nature of the phase transition is suggested to be continuous.