Solving fermion problems without solving the sign problem: symmetry-breaking wave functions from similarity-transformed propagators for solving 2D quantum dots

Abstract

It is well known that the use of the primitive second-order propagator in Path Integral Monte Carlo calculations of many-fermion systems leads to the sign problem. In this work, we show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ground state wave functions previously used in the study of quantum dots and quantum Hall effects. However, instead of localizing the electrons at positions which {\it minimize} the potential energy, this derivation shows that they should be located at positions which {\it maximize} the bosonic ground state wave function. Further improvements in the energy can be obtained by using these as initial wave functions in a Ground State Path-Integral Monte Carlo calculation with second and fourth-order propagators.