Projection Monte Carlo Method and Choice of the Optimal Trial Wavefunction

Abstract

We present here a brief and schematic description of a quantum Monte Carlo method for fermions. The ground state of a many-body fermion system is achieved by propagating in imaginary time a properly chosen trial wavefunction. It is shown that use of a trial wavefunction of definite total spin can enormously improve the convergence in imaginary time in the half filled Hubbard model. Fluctuations of the staggered magnetization become very small in a subspace of definite spin and large scale simulations are possible at a little expense of computer time. The antiferromagnetic broken symmetry state which occurs at half filling is the main reason of this and the physical consequences on the interpretation of the Mott insulator are discussed. Application of the methodology just away from half filling is also possible because good convergence in imaginary time is reached before the fermion sign problem becomes relevant.