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arXiv:2204.10062 · Journal of the Physical Society of Japan

Reply to Comments on “Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: A Quantum Monte Carlo Study”

Akiko Masaki-Kato, Yuichi Motoyama, Naoki Kawashima

Published May 18, 2022• 0 citations
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Abstract

We reply to the comments on our previous paper J. Phys. Soc. Jpn. 91, 024001 (2022)
DOI
10.7566/jpsj.91.066002

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Aji and Goldenfeld Reply:

Vivek Aji, Nigel D. Goldenfeld

This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson scaling relation and other known theoretical results, and explains the surprising results of dynamic Monte Carlo simulations in 3D for the vortex loop model. Our explanation, being based on identifying the correct relationship between real and Monte Carlo time, is not relevant for static Monte Carlo simulations, whose results do not need correction.

arXiv:cond-mat/0208410•Physical Review Letters•Aug 15, 2002•1 citation

Monte Carlo methods for impurity physics in ultracold Bose quantum gases

Luis A. Peña Ardila

Nature Reviews Physics•Mar 28, 2022•8 citations

The ground state of Bose gases with repulsive interaction: A quantum Monte Carlo study

Wirawan Purwanto, Shiwei Zhang

Bulletin of the American Physical Society•Mar 22, 2005•0 citations
We study dilute gases of interacting bosons at zero-temperature in the region where the system is characterized only by the s-wave scattering length. We carry out quantum Monte Carlo simulation of the Bose Hubbard model and a continuous-space hard-core model. Fitting the extended Lee-Huang-Yang formula to the Monte Carlo results establishes the detailed mapping from the lattice model to the continuous field theory characterized only by the s-wave scattering length. Our estimate of the intrinsic s-wave scattering length asa_sas​ of the Bose-Hubbard model is as/al=0.316(2)a_s/a_l = 0.316(2)as​/al​=0.316(2) where ala_lal​ is the lattice constant. It turned out that inclusion of the universal second correction term of O(nlog⁡n)O(n \log n)O(nlogn) makes the fitting worse while it is restored by inclusion of the non-universal third correction term, of which the existence was predicted analytically.
This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson scaling relation and other known theoretical results, and explains the surprising results of dynamic Monte Carlo simulations in 3D for the vortex loop model. Our explanation, being based on identifying the correct relationship between real and Monte Carlo time, is not relevant for static Monte Carlo simulations, whose results do not need correction.