Quantum Monte-Carlo Method without Negative-Sign Problem for Two-Dimensional Electron Systems under Strong Magnetic Fields

Abstract

The quantum Monte-Carlo method is applied to two-dimensional electron systems under strong magnetic fields. The negative-sign problem induced by this method can be avoided for certain filling factors by making a sign-problem-free Hamiltonian approximating the Coulomb-interaction Hamiltonian well. Our techniques for obtaining the sign-problem-free Hamiltonian are described in detail. Calculated results for the sign-problem-free Hamiltonian are also reported for Landau level filling ν=1⁄3 and are compared with those for the Coulomb-interaction Hamiltonian.