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

TL;DR

This paper introduces a method using similarity-transformed propagators to solve for the ground state of large 2D quantum dots with many fermions without encountering the sign problem, enabling more accurate quantum simulations.

Contribution

It presents a novel approach employing similarity-transformed propagators to avoid the sign problem in fermionic quantum Monte Carlo calculations of large quantum dots.

Findings

Successfully computed ground states of up to 100 polarized electrons.

Produced symmetry-breaking wave functions that maximize the bosonic ground state.

Improved energy estimates using these wave functions as initial states in Monte Carlo simulations.

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.