Quantum Monte-Carlo method without negative-sign problem for two-dimensional electron systems under strong magnetic fields

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.