Reweighting method for quantum Monte Carlo simulations with the negative-sign problem

Tota Nakamura, Naomichi Hatano, Hidetoshi Nishimori

Naomichi Hatano, Masuo Suzuki

Tota Nakamura, Naomichi Hatano, Hidetoshi Nishimori

We propose a new method for quantum Monte Carlo simulations with the negative-sign problem. In the conventional method, one simulates a virtual system whose Boltzmann factors are the absolute values of the original one, and analyzes the data so that the correct expression for physical quantities may be recovered. We simulate a different virtual system with properties closer to the original system and yet without the negative-sign problem. Comparison between the present method and the conventional one is made for the antiferromagnetic Heisenberg model on the 4×h4 square lattice with frustrations ( J 1 - J 2 model). We conclude that the present method is useful in the low-temperature region where the negative-sign problem becomes serious. It is also shown that the method is considerably efficient on the point that quantities for different parameters can be obtained in a single run.

Naomichi Hatano

Methods of analyzing data of quantum Monte Carlo simulations with the negative-sign problem are studied. It is pointed out that naive data analyses yield an overestimated statistical error or a quite unstable result. Two proper ways of analyzing the data are presented.

Yoshihiro Asai

Stephan Humeniuk, Yuan Wan

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudodensity matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudosnapshots of occupation numbers on large systems can be produced. There is a sign problem even when the conventional determinantal QMC algorithm can be made sign-problem free, and every pseudosnapshot comes with a sign and a reweighting factor. Nonetheless, this ``sampling sign problem'' turns out to be weak and manageable in a large, relevant parameter regime. The method allows one to compute distribution functions of arbitrary quantities defined in occupation number space and, from a practical point of view, facilitates the computation of complicated conditional correlation functions. While the projective measurements in quantum gas microscope experiments achieve direct sampling of occupation number states from the density matrix, the presented numerical method requires a Markov chain as an intermediate step and thus achieves only indirect sampling, but the full distribution of pseudosnapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements.